2026-04-13T13:22:05Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/9802025-07-17T12:55:38Zcom_2072_1033col_2072_452950

Regularity of radial minimizers and extremal solutions of semilinear elliptic equations Cabré Vilagut, Xavier Capella Kort, Antonio Partial differential equations Semi-stable radial solutions Local minimizers Extremal solutions Semilinear elliptic equations Reagularity theory Equacions en derivades parcials Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type We consider a special class of radial solutions of semilinear equations −?u = g(u) in the unit ball of Rn. It is the class of semi-stable solutions, which includes local minimizers, minimal solutions, and extremal solutions. We establish sharp pointwise, Lq, and Wk,q estimates for semi-stable radial solutions. Our regularity results do not depend on the specific nonlinearity g. Among other results, we prove that every semi-stable radial weak solution u ? H1 0 is bounded if n ? 9 (for every g), and belongs to H3 = W3,2 in all dimensions n (for every g increasing and convex). The optimal regularity results are strongly related to an explicit exponent which is larger than the critical Sobolev exponent. Peer Reviewed 2005 Article Open Access