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• W2049565573 abstract "Boundary regularity of solutions of the fully nonlinear boundary value problem <disp-formula content-type=math/mathml> [ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F left-parenthesis x comma u comma upper D u comma upper D squared u right-parenthesis equals 0 in normal upper Omega comma upper G left-parenthesis x comma u comma upper D u right-parenthesis equals 0 on partial-differential normal upper Omega> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mi>u</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width=1em /> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext>in</mml:mtext> </mml:mrow> <mml:mspace width=thickmathspace /> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:mo>,</mml:mo> <mml:mspace width=2em /> <mml:mi>G</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width=1em /> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext>on</mml:mtext> </mml:mrow> <mml:mspace width=thickmathspace /> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>F(x,u,Du,{D^2}u) = 0quad {text {in}};Omega ,qquad G(x,u,Du) = 0quad {text {on}};partial Omega</mml:annotation> </mml:semantics> </mml:math> ] </disp-formula> is discussed for two-dimensional domains <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega> <mml:semantics> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:annotation encoding=application/x-tex>Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=application/x-tex>F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is assumed uniformly elliptic and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is assumed to depend (in a nonvacuous manner) on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D u> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>u</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>Du</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Continuity estimates are proved for first and second derivatives of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=u> <mml:semantics> <mml:mi>u</mml:mi> <mml:annotation encoding=application/x-tex>u</mml:annotation> </mml:semantics> </mml:math> </inline-formula> under weak hypotheses for smoothness of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=application/x-tex>F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</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=normal upper Omega> <mml:semantics> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:annotation encoding=application/x-tex>Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W2049565573 date "1987-01-01" @default.
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• W2049565573 title "Two-dimensional nonlinear boundary value problems for elliptic equations" @default.
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