| 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 |
| Externí odkaz: |
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