Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A priori estimates for positive solutions to subcritical elliptic problems in a class of non-convex regions

Pages: 783 - 790, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017038

       Abstract        References        Full Text (724.6K)       Related Articles       

Alfonso Castro - Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States (email)
Rosa Pardo - Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040-Madrid, Spain (email)

Abstract: Building on the a priori estimates established in [3], we obtain a priori estimates for classical solutions to elliptic problems with Dirichlet boundary conditions on regions with convex-starlike boundary. This includes ring-like regions. Arguments that go back to [4] are used to prove a priori bounds near the convex part of the boundary. Using that the boundary term in the Pohozaev identity on the boundary of a star-like region does not change sign, the proof is concluded.

Keywords:  A priori estimates, positive solutions, subcritical exponents, ring-like region, moving planes method, Kelvin transform.
Mathematics Subject Classification:  Primary: 35B45; Secondary: 35B09, 35B33, 35J25, 35J60.

Received: September 2015;      Revised: October 2016;      Available Online: January 2017.