Isolated boundary singularities of semilinear elliptic equations
(2011) Calculus of Variations and Partial Differential Equations — Vol. 40, n° 1-2, p. 183-221 (2011)
Files
17.pdf
Open Access - Adobe PDF
- 326.11 KB
Details
- Authors
- Abstract
- Given a smooth domain Omega subset of R-N such that 0 is an element of partial derivative Omega and given a nonnegative smooth function zeta on partial derivative Omega, we study the behavior near 0 of positive solutions of -Delta u = u(q) in Omega such that u = zeta on partial derivative Omega{0}. We prove that if N+1/N-1 < q < N-2/N-2, then u(x) <= C broken vertical bar x broken vertical bar(-2/q-1) and we compute the limit of broken vertical bar x broken vertical bar(-2/q-1)u(x) as x -> 0. We also investigate the case q = N+1/N-1 . The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains.
- Affiliations
Université François Rabelais Laboratoire de Mathématiques et Physique Théorique
Citations
Ponce, A., Véron, L., & Bidaut-Véron, M.-F. (2011). Isolated boundary singularities of semilinear elliptic equations. Calculus of Variations and Partial Differential Equations, 40(1-2), 183-221. https://doi.org/10.1007/s00526-010-0337-z (Original work published 2011)