Boundary unique continuation theorems under zero Neumann boundary conditions

DOI10.1017/S0004972700034882zbMath1087.35019MaRDI QIDQ5694930

Song Yan Zhang, Xiang Xing Tao

Publication date: 5 October 2005

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Lipschitz domainsboundary doubling propertyKato-Fefferman-Phong class

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs with low regular coefficients and/or low regular data (35R05) Boundary behavior of harmonic functions in higher dimensions (31B25) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (11)

Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations ⋮ Unique continuation from a crack's tip under Neumann boundary conditions ⋮ Unique continuation from the edge of a crack ⋮ Uniqueness and reconstruction for the fractional Calderón problem with a single measurement ⋮ Unique continuation principles in cones under nonzero Neumann boundary conditions ⋮ Quantitative unique continuation for Robin boundary value problems on C^{1,1} domains ⋮ On simple eigenvalues of the fractional Laplacian under removal of small fractional capacity sets ⋮ Unique continuation and classification of blow-up profiles for elliptic systems with Neumann boundary coupling and applications to higher order fractional equations ⋮ Asymptotic expansions and unique continuation at Dirichlet-Neumann boundary junctions for planar elliptic equations ⋮ Unique continuation principles for a higher order fractional Laplace equation ⋮ Spacetime harmonic functions and the mass of 3-dimensional asymptotically flat initial data for the Einstein equations

Cites Work

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• A partial answer to a conjecture of B. Simon concerning unique continuation
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Convex domains and unique continuation at the boundary
• Harnack's Inequality for Schrodinger Operators and the Continuity of Solutions
• Schrödinger semigroups
• A unique continuation theorem for uniformly elliptic equations with strongly singular potentials
• Unique continuation for elliptic operators: A geometric-variational approach
• Brownian motion and harnack inequality for Schrödinger operators
• A unique continuation theorem for the Schrödinger equation with singular magnetic field
• Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields

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