Green's function, caloric measure and Fatou theorem for nondivergence parabolic equations in non cylindrical domains

DOI10.1515/FORUM.2008.011zbMath1165.35005MaRDI QIDQ3516707

Roberto Argiolas, Anna Piro Grimaldi

Publication date: 11 August 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

zbMATH Keywords

parabolic equationGreen functioncaloric measuredoubling propertiescomparison theorems of Harnack type

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order parabolic equations (35K20) Integral representations of solutions to PDEs (35C15) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (4)

A Quantitative Regularity Estimate for Nonnegative Supersolutions of Uniformly Parabolic Equations ⋮ The Dirichlet problem for second order parabolic operators in non-cylindrical domains ⋮ Regularity of the Solutions for Parabolic Two-Phase Free Boundary Problems ⋮ Two‐Phase Free Boundary Problems for Parabolic Operators: Smoothness of the Front

Cites Work

• Positive solutions of elliptic equations in nondivergence form and their adjoints
• The \(L^ p\)-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations
• Regularity of the free boundary in parabolic phase-transition problems
• Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems
• Area Integral Estimates for Caloric Functions
• Behavior near the boundary of positive solutions of second order parabolic equations. II
• The 𝐿^{𝑝} Dirichlet problem and nondivergence harmonic measure
• Temperatures in Several Variables: Kernel Functions, Representations, and Parabolic Boundary Values

This page was built for publication: Green's function, caloric measure and Fatou theorem for nondivergence parabolic equations in non cylindrical domains