Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589519 | Journal of Functional Analysis | 2017 | 54 Pages |
Abstract
We give necessary and sufficient conditions for the existence of weak solutions to the model equation−Δpu=σuqonRn, in the case 00b>0. These results are new even in the classical case p=2p=2.Our approach is based on the use of special nonlinear potentials of Wolff type adapted for “sublinear” problems, and related integral inequalities. It allows us to treat simultaneously several problems of this type, such as equations with general quasilinear operators divA(x,∇u), fractional Laplacians (−Δ)α(−Δ)α, or fully nonlinear k-Hessian operators.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dat Cao, Igor Verbitsky,