Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms
Tomasz Klimsiak, Andrzej Rozkosz (2016)
Colloquium Mathematicae
Similarity:
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...