Mathematics

Existence results for p(x)-Laplace equations

Al. S. Tersenov

University of Crete

Abstract: The non-homogeneous Dirichlet problem for degenerate quasilinear parabolic equations is considered. We prove the existence of a solution u such that ut belongs to L∞. The L∞ estimate of ut is obtained by introducing a new time variable.

Keywords: degenerate parabolic equations, a priori estimates, generalized solutions

UDC: 517.95

Received: 16.10.2024
Accepted: 06.12.2024

Language: English

DOI: 10.25587/2411-9326-2024-4-106-117