Uniqueness and stability of extension of solution of an elliptic equation from a set to a domain
β Scribed by N. S. Nadirashvili
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1986
- Tongue
- English
- Weight
- 382 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0001-4346
No coin nor oath required. For personal study only.
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## Abstract Given a __C__^2^ function __u__, we consider its quasiβconvex envelope __u__\* and we investigate the relationship between __D__^2^__u__ and __D__^2^__u__\* (the latter intended in viscosity sense); we obtain two inequalities between the tangential Laplacian of __u__ and __u__\* and the
In this paper, we deal with the sublinear elliptic equation: -βu+V (x)u+a(x)|u| p sgn(u) = f on R N , N > 2, 0 < p < 1. Under suitable assumptions on the terms V and a, we prove some existence, uniqueness and multiplicity results. Continuity of solutions in the perturbation parameter f at 0 is also