Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms

• Autorzy: Tomasz Klimsiak , Andrzej Rozkosz
• Języki publikacji: EN

Abstrakty

EN

We are mainly concerned with equations of the form -Lu = f(x,u) + μ, where L is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, f satisfies the monotonicity condition and mild integrability conditions, and μ is a bounded smooth measure. We prove general results on existence, uniqueness and regularity of probabilistic solutions, which are expressed in terms of solutions to backward stochastic differential equations. Applications include equations with nonsymmetric divergence form operators, with gradient perturbations of some pseudodifferential operators and equations with Ornstein-Uhlenbeck type operators in Hilbert spaces. We also briefly discuss the existence and uniqueness of probabilistic solutions in the case where L corresponds to a lower bounded semi-Dirichlet form.

Kategorie tematyczne

• 35R06: Partial differential equations with measure
• 35J61: Semilinear elliptic equations
• 60H30: Applications of stochastic analysis (to PDE, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 145
• Numer: 1
• Strony: 35-67

Daty

wydano

2016

Twórcy

autor

Tomasz Klimsiak

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

Andrzej Rozkosz

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/cm6466-10-2015