A regularity criterion for positive weak solutions of −Δu=uα
✍ Scribed by F. Pacard
- Book ID
- 110557906
- Publisher
- European Mathematical Society
- Year
- 1993
- Tongue
- English
- Weight
- 338 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0010-2571
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📜 SIMILAR VOLUMES
We use the stochastic process called the Brownian snake to investigate solutions of the partial differential equation ∆u = u 2 in a domain D of class C 2 of the plane. We prove that nonnegative solutions are in one-to-one correspondence with pairs (K, ν) where K is a closed subset of ∂D and ν is a R
## Abstract In this paper, we consider the semilinear elliptic problem where Ω⊂ℝ^N^ (__N__⩾3) is a bounded smooth domain such that 0∈Ω, σ>0 is a real parameter, $$\mu < \overline{\mu } = (N - 2)^{2} /4$$ and __f__(__x__) is some given function in L^∞^(Ω) such that __f__(__x__)⩾0, __f__(__x__)≢0 i