Green Functions, Potentials, and the Dirichlet Problem for the Heat Equation

DOI10.1112/plms/s3-33.2.251zbMath0336.35046OpenAlexW2031874666MaRDI QIDQ4104316

Neil A. Watson

Publication date: 1976

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/s3-33.2.251

Mathematics Subject Classification ID

Heat equation (35K05) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Potentials and capacities on other spaces (31C15) Connections of harmonic functions with differential equations in higher dimensions (31B35) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (33)

Kernels and Choquet capacities ⋮ A Hausdorff measure classification of polar sets for the heat equation ⋮ On Parabolic Measures and Subparabolic Functions ⋮ Density of extremal measures in parabolic potential theory ⋮ Nonlinear parabolic capacity and polar sets of superparabolic functions ⋮ Singular and quasi-bounded functions associated with the heat equation ⋮ Unnamed Item ⋮ REGULARITY OF BOUNDARY POINTS IN THE DIRICHLET PROBLEM FOR THE HEAT EQUATION ⋮ Convexity of mean values of non-negative subtemperatures ⋮ A constant rank theorem for spacetime convex solutions of heat equation ⋮ The set of mildly regular boundary points has full caloric measure ⋮ On the essential boundary and supports of harmonic measures for the heat equation ⋮ On heat capacity and parabolic measure ⋮ Irregularity of bondary points in the Dirichlet problem for the heat equation ⋮ A characterization of heat balls by a mean value property for temperatures ⋮ Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation ⋮ Brownian motion and thermal capacity ⋮ Removable singularities of semilinear parabolic equations ⋮ Pointwise bounds and blow-up for systems of semilinear parabolic inequalities and nonlinear heat potential estimates ⋮ Mean values of subtemperatures over level surfaces of Green functions ⋮ CALORIC MEASURE FOR ARBITRARY OPEN SETS ⋮ An Example on Null Sets of Parabolic Measures ⋮ Dimension of fractional Brownian motion with variable drift ⋮ Uniqueness and representation theorems for the inhomogeneous heat equation ⋮ Caloric Measure Null Sets ⋮ Representation formulae for nonhomogeneous differential operators and applications to PDEs ⋮ Unnamed Item ⋮ Wiener's criterion for the heat equation ⋮ THERMIC MINORANTS AND REDUCTIONS OF SUPERTEMPERATURES ⋮ A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain ⋮ Parabolic potential theory ⋮ UNIQUENESS OF EXTENDABLE TEMPERATURES ⋮ The weak maximum principle for parabolic differential inequalities

This page was built for publication: Green Functions, Potentials, and the Dirichlet Problem for the Heat Equation