On the Laplace equation with a supercritical nonlinear Robin boundary condition in the half-space

Author(s)

Ferreira, Lucas C. F. ^[1] ; Medeiros, Everaldo S. ^[2] ; Montenegro, Marcelo ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba - Brazil

• Document type: Journal article
• Source: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 47, n. 3-4, p. 667-682, JUL 2013.
• Web of Science Citations: 1

Abstract

We study the Laplace equation in the half-space with a nonlinear supercritical Robin boundary condition on , where n a parts per thousand yen 3 and lambda a parts per thousand yen 0. Existence of solutions is obtained by means of a fixed point argument for a small data . The indexes p, q are chosen for the norm to be invariant by scaling of the boundary problem. The solution u is positive whether f(x) > 0 a.e. . When f is radially symmetric, u is invariant under rotations around the axis [x (n) = 0]. Moreover, in a certain L (q) -norm, we show that solutions depend continuously on the parameter lambda a parts per thousand yen 0. (AU)

• FAPESP's process: 10/19098-2 - Singular solutions, symmetries and self-similarity for PDEs
• Grantee: Lucas Catão de Freitas Ferreira
• Support Opportunities: Regular Research Grants