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• W1567763844 abstract "We examine the possible extensions to the Lipschitzian setting of the classical result on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-convergence: first (approximation), if a sequence <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis f Subscript n Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(f_n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of functions of class <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> from <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R Superscript upper N> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>mathbb {R}^N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbb {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> converges uniformly to a function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of class <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then the gradient of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a limit of gradients of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Subscript n> <mml:semantics> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>f_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the sense that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=g r a p h left-parenthesis nabla f right-parenthesis subset-of limit inf g r a p h left-parenthesis nabla f Subscript n Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>graph</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:munder> <mml:mo movablelimits=true form=prefix>lim inf</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mo>+</mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:munder> <mml:mi>graph</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>operatorname {graph}(nabla f)subset liminf _{nto +infty } operatorname {graph}(nabla f_n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; second (regularization), the functions <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis f Subscript n Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(f_n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can be chosen to be of class <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript normal infinity> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-converging to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the sense that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=limit Underscript n right-arrow plus normal infinity Endscripts double-vertical-bar f Subscript n Baseline minus f double-vertical-bar Subscript normal infinity Baseline plus double-vertical-bar nabla f Subscript n Baseline minus nabla f double-vertical-bar Subscript normal infinity Baseline equals 0> <mml:semantics> <mml:mrow> <mml:munder> <mml:mo movablelimits=true form=prefix>lim</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mo>+</mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:munder> <mml:mo fence=false stretchy=false>‖<!-- ‖ --></mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>−<!-- − --></mml:mo> <mml:mi>f</mml:mi> <mml:msub> <mml:mo fence=false stretchy=false>‖<!-- ‖ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:mo fence=false stretchy=false>‖<!-- ‖ --></mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>−<!-- − --></mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:mi>f</mml:mi> <mml:msub> <mml:mo fence=false stretchy=false>‖<!-- ‖ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>lim _{nto +infty } |f_n-f|_{infty }+ |nabla f_n-nabla f|_{infty }=0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In other words, the space of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript normal infinity> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> functions is dense in the space of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> functions endowed with the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> pseudo-norm. We first deepen the properties of Warga’s counterexample (1981) for the extension of the approximation part to the Lipschitzian setting. This part cannot be extended, even if one restricts the approximation schemes to the classical convolution and the Lasry-Lions regularization. We thus make more precise various results in the literature on the convergence of subdifferentials. We then show that the regularization part can be extended to the Lipschitzian setting, namely if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f colon double-struck upper R Superscript upper N Baseline right-arrow double-struck upper R> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>f:mathbb {R}^N rightarrow {mathbb R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a locally Lipschitz function, we build a sequence of smooth functions <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis f Subscript n Baseline right-parenthesis Subscript n element-of double-struck upper N> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>N</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>(f_n)_{n in mathbb {N}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <disp-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartLayout 1st Row 1st Column Blank 2nd Column a m p semicolon 3rd Column a m p semicolon limit Underscript n right-arrow plus normal infinity Endscripts double-vertical-bar f Subscript n Baseline minus f double-vertical-bar Subscript normal infinity Baseline equals 0 comma 2nd Row 1st Column Blank 2nd Column a m p semicolon 3rd Column a m p semicolon limit Underscript n right-arrow plus normal infinity Endscripts d Subscript upper H a u s Baseline left-parenthesis g r a p h left-parenthesis nabla f Subscript n Baseline right-parenthesis comma g r a p h left-parenthesis partial-differential f right-parenthesis right-parenthesis equals 0 period EndLayout> <mml:semantics> <mml:mtable columnalign=right center left rowspacing=3pt columnspacing=0 thickmathspace side=left displaystyle=true> <mml:mtr> <mml:mtd /> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:munder> <mml:mo movablelimits=true form=prefix>lim</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mo>+</mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:munder> <mml:mo fence=false stretchy=false>‖<!-- ‖ --></mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>−<!-- − --></mml:mo> <mml:mi>f</mml:mi> <mml:msub> <mml:mo fence=false stretchy=false>‖<!-- ‖ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd /> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:munder> <mml:mo movablelimits=true form=prefix>lim</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mo>+</mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:munder> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>H</mml:mi> <mml:mi>a</mml:mi> <mml:mi>u</mml:mi> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>graph</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>graph</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0.</mml:mn> </mml:mtd> </mml:mtr> </mml:mtable> <mml:annotation encoding=application/x-tex>begin{eqnarray*} &&lim _{nto +infty } |f_n-f|_{infty }=0, &&lim _{nto +infty } d_{Haus}(operatorname {graph}(nabla f_n), operatorname {graph}(partial f))=0. end{eqnarray*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> In other words, the space of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript normal infinity> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> functions is dense in the space of locally Lipschitz functions endowed with an appropriate Lipschitz pseudo-distance. Up to now, Rockafellar and Wets (1998) have shown that the convolution procedure permits us to have the equality <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=limit sup g r a p h left-parenthesis nabla f Subscript n Baseline right-parenthesis equals g r a p h left-parenthesis partial-differential f right-parenthesis> <mml:semantics> <mml:mrow> <mml:munder> <mml:mo movablelimits=true form=prefix>lim sup</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mo>+</mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:munder> <mml:mi>graph</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>graph</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>limsup _{nto +infty } operatorname {graph}(nabla f_n) =operatorname {graph}(partial f)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which cannot provide the exactness of our result. As a consequence, we obtain a similar result on the regularization of epi-Lipschitz sets. With both functional and set parts, we improve previous results in the literature on the regularization of functions and sets." @default.
• W1567763844 created "2016-06-24" @default.
• W1567763844 creator A5000713548 @default.
• W1567763844 creator A5071460705 @default.
• W1567763844 date "2006-05-09" @default.
• W1567763844 modified "2023-09-25" @default.
• W1567763844 title "Approximation and regularization of Lipschitz functions: Convergence of the gradients" @default.
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• W1567763844 cites W2015386597 @default.
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• W1567763844 cites W2045947709 @default.
• W1567763844 cites W2048564717 @default.
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• W1567763844 cites W4235022435 @default.
• W1567763844 cites W4237476430 @default.
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• W1567763844 cites W4249513058 @default.
• W1567763844 cites W53137934 @default.
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• W1567763844 doi "https://doi.org/10.1090/s0002-9947-06-04103-1" @default.
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