On semilinear elliptic equations with diffuse measures
| Autor: | Andrzej Rozkosz, Tomasz Klimsiak |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
35J61
35R06 Pure mathematics Dirichlet form Applied Mathematics Operator (physics) 010102 general mathematics Function (mathematics) 01 natural sciences Measure (mathematics) Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Analysis Mathematics Sign (mathematics) Analysis of PDEs (math.AP) |
| Popis: | We consider semilinear equation of the form $$-Lu=f(x,u)+\mu $$ , where L is the operator corresponding to a transient symmetric regular Dirichlet form $${\mathcal {E}}$$ , $$\mu $$ is a diffuse measure with respect to the capacity associated with $${\mathcal {E}}$$ , and the lower-order perturbing term f(x, u) satisfies the sign condition in u and some weak integrability condition (no growth condition on f(x, u) as a function of u is imposed). We prove the existence of a solution under mild additional assumptions on $${\mathcal {E}}$$ . We also show that the solution is unique if f is nonincreasing in u. |
| Databáze: | OpenAIRE |
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