Nonlinear Parabolic Problems in Anisotropic Sobolev Spaces

Year 2024, Volume: 14 Issue: 2, 109 - 143, 31.07.2024

Mohammed El Ansari Youssef Akdim

Abstract

In this paper, our goal is to establish results on existence of renormalized
solutions for a class of Stefan problems of the form β(u)t − div(a(x, Du) + F(u)) ∋ f,
posed in an open bounded Ω, where data belongs to L
1 −data, β is a maximal monotone graph and div(a(x, Du)) is a Leary-Lions operator with anisotropic growth conditions.

Keywords

anisotropic Sobolev spaces, maximal monotone graph, Stefan type problems

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