Renormalized solutions of semilinear elliptic equations with general measure data
| Autor: | Andrzej Rozkosz, Tomasz Klimsiak |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Primary: 35D99. Secondary: 35J61
60H30 010505 oceanography Dirichlet form General Mathematics 010102 general mathematics Duality (optimization) Absolute continuity 01 natural sciences Measure (mathematics) Kernel (algebra) Elliptic curve Mathematics - Analysis of PDEs Operator (computer programming) FOS: Mathematics Applied mathematics 0101 mathematics 0105 earth and related environmental sciences Resolvent Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1609.00922 |
| Popis: | In the paper, we first propose a definition of renormalized solution of semilinear elliptic equation involving operator corresponding to a general (possibly nonlocal) symmetric regular Dirichlet form satisfying the so-called absolute continuity condition and general (possibly nonsmooth) measure data. Then we analyze the relationship between our definition and other concepts of solutions considered in the literature (probabilistic solutions, solution defined via the resolvent kernel of the underlying Dirichlet form, Stampacchia's definition by duality). We show that under mild integrability assumption on the data all these concepts coincide. |
| Databáze: | OpenAIRE |
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