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• W2093892008 abstract "Let <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> denote a smooth domain in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper R Superscript n> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{R^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> containing the closure of a convex polyhedron <italic>D</italic>. Set <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=chi Subscript upper D> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>χ<!-- χ --></mml:mi> <mml:mi>D</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{chi _D}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> equal to the characteristic function of <italic>D</italic>. We find a flux <italic>g</italic> so that if <italic>u</italic> is the nonconstant solution of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d i v left-parenthesis left-parenthesis 1 plus chi Subscript upper D Baseline right-parenthesis nabla u right-parenthesis equals 0> <mml:semantics> <mml:mrow> <mml:mi>div</mml:mi> <mml:mspace width=thickmathspace /> <mml:mo stretchy=false>(</mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>χ<!-- χ --></mml:mi> <mml:mi>D</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> <mml:mi mathvariant=normal>∇<!-- ∇ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>operatorname {div};((1 + {chi _D})nabla u) = 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in <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> with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartFraction partial-differential u Over partial-differential n EndFraction equals g> <mml:semantics> <mml:mrow> <mml:mfrac> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfrac> <mml:mo>=</mml:mo> <mml:mi>g</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>frac {{partial u}}{{partial n}} = g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=partial-differential normal upper Omega> <mml:semantics> <mml:mrow> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>partial Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <italic>D</italic> is uniquely determined by the Cauchy data <italic>g</italic> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f identical-to u slash partial-differential normal upper Omega> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>≡<!-- ≡ --></mml:mo> <mml:mi>u</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>f equiv u/partial Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W2093892008 title "The inverse conductivity problem with one measurement: uniqueness for convex polyhedra" @default.
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