Existence of weak solutions to doubly degenerate diffusion equations
✍ Scribed by Aleš Matas; Jochen Merker
- Publisher
- Springer-Verlag
- Year
- 2012
- Tongue
- English
- Weight
- 274 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0862-7940
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📜 SIMILAR VOLUMES
In this paper, we study the problem -div a(x; u; ∇u) -div (u) + g(x; u) = f in in the setting of the weighted sobolev space W 1;p 0 ( ; ). The main novelty of our work is L ∞ estimates on the solutions, and the existence of a weak and renormalized solution.
This paper deals with a class of degenerate quasilinear elliptic equations of the form -div(a(x, u, ∇u) = gdiv(f ), where a(x, u, ∇u) is allowed to be degenerate with the unknown u. We prove existence of bounded solutions under some hypothesis on f and g. Moreover we prove that there exists a renor