Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain inR2with Robin Boundary Conditions

DOI10.1080/00036810108840902zbMath1033.35030OpenAlexW2080279738MaRDI QIDQ2729534

Elsayed M. E. Zayed

Publication date: 22 July 2001

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810108840902

zbMATH Keywords

inverse problemSchrödinger equationtrace formulaRobin problemheat expansionclassical ideal gas

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (6)

An inverse eigenvalue problem of the wave equation for a multi-connected region in \(\mathbb{R}^{2}\) together with three different types of boundary conditions ⋮ Short-time asymptotics of the two-dimensional wave equation for an annular vibrating membrane with applications in the mathematical physics ⋮ Short-time asymptotics of the heat kernel on bounded domain with piecewise smooth boundary conditions and its applications to an ideal gas ⋮ An inverse problem for a general vibrating annular membrane in \(\mathbb R^ 3\) with its physical applications: further results. ⋮ An inverse problem for the three-dimensional multi-connected vibrating membrane with Robin boundary conditions. ⋮ On hearing the shape of a general multi-connected vibrating membrane in \(\mathbb R^2\) with piecewise smooth positive functions in the Robin boundary conditions.

Cites Work

• Hearing the shape of a general convex domain
• Heat equation for an arbitrary doubly-connected region in \(R^ 2\) with mixed boundary conditions
• An inverse eigenvalue problem for a general convex domain
• The asymptotics of the heat equation for a boundary value problem
• Distribution of eigenfrequencies for the wave equation in a finite domain. I.: Three-dimensional problem with smooth boundary surface
• An asymptotic expansion for the heat equation
• A study of certain Green's functions with applications in the theory of vibrating membranes
• Heat Equation for an Arbitrary Multiply-Connected Region in R² with Impedance Boundary Conditions
• Eigenvalues of the Laplacian with Neumann boundary conditions
• On hearing the shape of an arbitrary doubly-connected region in R²
• An inverse problem for a general multiply connected bounded domain
• Can One Hear the Shape of a Drum?

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