Global Hölder Solvability of parabolic equations on domains with capacity density conditions
Abstract
We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally Hölder continuous solutions. Notably, our results accommodate data exhibiting singularities nearly as critical as the inverse square of the distance from the boundary.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Differential Equations and Boundary Problems
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 6 January 2026
- Document type
- Preprint