A Fatou Theorem for the Solution of the Heat Equation at the Corner Points of a Cylinder
From MaRDI portal
Publication:4015879
DOI10.2307/2154051zbMath0763.35043OpenAlexW4249242961MaRDI QIDQ4015879
Publication date: 7 December 1992
Full work available at URL: https://doi.org/10.2307/2154051
Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) Integral representations of solutions to PDEs (35C15) A priori estimates in context of PDEs (35B45) Initial value problems for second-order parabolic equations (35K15) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Boundary behavior of harmonic functions in higher dimensions (31B25)
Related Items
The boundary behavior of heat kernels of Dirichlet Laplacians ⋮ The global behavior of heat kernels in exterior domains ⋮ Initial blow-up of solutions of semilinear parabolic inequalities ⋮ Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem ⋮ Blow-up phenomena in nonlocal eigenvalue problems: when theories of \(L^1\) and \(L^2\) meet ⋮ Another proof for the removable singularities of the heat equation ⋮ Comparison of Green functions and harmonic measures for parabolic operators ⋮ Estimates of Dirichlet heat kernel for symmetric Markov processes
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations
- Non-negative solutions of generalized porous medium equations
- The Green function for uniformly elliptic equations
- Estimates of Caloric Measure and the Initial-Dirichlet Problem for the Heat Equation in Lipschitz Cylinders
- Nonnegative Solutions of the Initial-Dirichlet Problem for Generalized Porous Medium Equations in Cylinders
- Boundary behavior of temperatures I
- Temperatures in Several Variables: Kernel Functions, Representations, and Parabolic Boundary Values
- On the Solutions of the Equation of Heat Conduction
