Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772422 | Journal of Functional Analysis | 2017 | 47 Pages |
Abstract
In the paper we consider elliptic equations of the form âAu=uâγâ
μ, where A is the operator associated with a regular symmetric Dirichlet form, μ is a positive nontrivial measure and γ>0. We prove the existence and uniqueness of solutions of such equations as well as some regularity results. We also study stability of solutions with respect to the convergence of measures on the right-hand side of the equation. For this purpose, we introduce some type of functional convergence of smooth measures, which in fact is equivalent to the quasi-uniform convergence of associated potentials.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Tomasz Klimsiak,