Perturbation of domains and Green kernels of heat equations

DOI10.3792/pjaa.54.322zbMath0432.35003OpenAlexW2093081077MaRDI QIDQ1138709

Shin Ozawa

Publication date: 1978

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.54.322

zbMATH Keywords

heat equationfundamental solutiontraceDirichlet boundary conditionvariationGreen kernelsasymptotics of eigenfunctions of the Laplacianperturbation of domains

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Fundamental solutions to PDEs (35A08) Heat equation (35K05) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items

Quantum ergodicity of boundary values of eigenfunctions, Hadamard variational formula for eigenvalues of the Stokes equations and its application, Remarks on Hadamard's variation of eigenvalues of the Laplacian, Perturbation of domains and Green kernels of heat equations. II, Perturbation of domains and Green kernels of heat equations. III, Hadamard variational formula for the Green's function of the boundary value problem on the Stokes equations, Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions, New approach to the Hadamard variational formula for the Green function of the Stokes equations, Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains

Cites Work

• The Hadamard variational formula for the Green functions of some normal elliptic boundary value problems
• Convexity of domain functionals
• The Resolvent of an Elliptic Boundary Problem
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
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