We develop a simple variational argument based on the usual Nirenberg difference quotient technique to deal with the regularity of the solutions of Dirichlet and Neumann problems for some linear and quasilinear elliptic equation in Lipschitz domains. We obtain optimal regularity results in the natur
Monotonicity for elliptic equations in unbounded Lipschitz domains
β Scribed by H. Berestycki; L. A. Caffarelli; L. Nirenberg
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 243 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0010-3640
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## Abstract We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semiβexplicit representation formulas via operatorβvalued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative r
In this paper we study an elliptic linear operator in weighted Sobolev spaces and show existence and uniqueness theorems for the Dirichlet problem when the coefficients are given in suitable spaces of Morrey type, improving the previous results known in the literature.
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