Nonlinear Parabolic Problems in Anisotropic Sobolev Spaces

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

References

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