Renormalized solutions of semilinear equations involving measure data and operator corresponding to Dirichlet form

Autor: Klimsiak, Tomasz, Rozkosz, Andrzej
Rok vydání: 2015
Předmět:
Zdroj: NoDEA Nonlinear Differential Equations Appl. 22 (2015) 1911--1934
Druh dokumentu: Working Paper
DOI: 10.1007/s00030-015-0350-1
Popis: We generalize the notion of renormalized solution to semilinear elliptic and parabolic equations involving operator associated with general (possibly nonlocal) regular Dirichlet form and smooth measure on the right-hand side. We show that under mild integrability assumption on the data a quasi-continuous function $u$ is a renormalized solution to an elliptic (or parabolic) equation in the sense of our definition iff $u$ is its probabilistic solution, i.e. $u$ can be represented by a suitable nonlinear Feynman-Kac formula. This implies in particular that for a broad class of local and nonlocal semilinear equations there exists a unique renormalized solution.
Databáze: arXiv
načítá se...