<p>In this paper, we prove that the knowledge of the Dirichlet-to-Neumann map, measured on the full boundary of the bounded domain in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2090_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> <mo>,</mo> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{R}^{n}, n\geq 3$</EquationSource> </InlineEquation>, can uniquely determine the Taylor series of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2090_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>a</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$a(x,z)$</EquationSource> </InlineEquation> at <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2090_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>z</mi> <mo>=</mo> <mn>0</mn> </math></EquationSource> <EquationSource Format="TEX">$z=0$</EquationSource> </InlineEquation> under general assumptions on <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2090_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>a</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$a(x,z)$</EquationSource> </InlineEquation>.</p>

Global uniqueness for a semilinear biharmonic equation

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2025年8月4日

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Yanjun Ma,
Hongxiang Zhang

摘要

In this paper, we prove that the knowledge of the Dirichlet-to-Neumann map, measured on the full boundary of the bounded domain in $R^{n}, n \geq 3$ $\mathbb{R}^{n}, n\geq 3$ , can uniquely determine the Taylor series of $a (x, z)$ $a(x,z)$ at $z = 0$ $z=0$ under general assumptions on $a (x, z)$ $a(x,z)$ .