Renormalized solutions of semilinear equations involving measure data and operator corresponding to Dirichlet form
Autor: | Klimsiak, Tomasz, Rozkosz, Andrzej |
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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 |
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