Heat flow and Brownian motion for a region in \({\mathbb{R}}^ 2\) with a polygonal boundary

DOI10.1007/BF01207512zbMath0682.60067MaRDI QIDQ1824285

S. Srisatkunarajah, Michiel van den Berg

Publication date: 1990

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviourheat conduction problempolygonal boundary

Mathematics Subject Classification ID

Brownian motion (60J65) Heat equation (35K05) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (17)

Asymptotics for the spectral heat function and bounds for integrals of Dirichlet eigenfunctions ⋮ Heat content and Brownian motion for some regions with a fractal boundary ⋮ On the heat content of a polygon ⋮ Heat flow out of regions in \({\mathbb{R}}^ m\) ⋮ On the Placement of an Obstacle so as to Optimize the Dirichlet Heat Content ⋮ Heat content asymptotics for Riemannian manifolds with Zaremba boundary conditions ⋮ Heat flow in polygons with reflecting edges ⋮ Heat flow from polygons ⋮ Average error for spectral asymptotics on surfaces ⋮ Heat content determines planar triangles ⋮ Heat invariants for odd-dimensional hemispheres ⋮ Neumann heat content asymptotics with singular initial temperature and singular specific heat ⋮ Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions ⋮ Growth of heat trace and heat content asymptotic coefficients ⋮ Isospectrality and heat content ⋮ On efficiency and localisation for the torsion function ⋮ Mean curvature and the heat equation

Cites Work

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• Sur une conjecture de M. Kac. (On a conjecture of M. Kac)
• Curvature and the eigenvalues of the Laplacian
• Some Theorems Concerning 2-Dimensional Brownian Motion
• Heat Equation for a Region in R² with a Polygonal Boundary
• Some asymptotic formulas involving capacity
• Electrostatic capacity, heat flow, and brownian motion
• Can One Hear the Shape of a Drum?
• Note on a Heat Conduction Problem

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