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

Quasi-regular Dirichlet forms: Examples and counterexamples

We prove some new results on quasi-regular Dirichlet forms. These include results on perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness implies the existence of an associated right continuous strong Markov process. We also discuss applications to a number of examples including cases with possibly degenerate (sub)-elliptic part, diffusions on loops spaces, an...

Quasi-Regular Dirichlet Forms and Applications

Since the celebrated result of Fukushima on the connection between regular Dirichlet forms and Hunt processes in 1971, the theory of Dirichlet forms has been rapidly developed and has brought a wide range of applications in various related areas of mathematics and physics (see e.g. the three new books [BH 91], [MR 92], [FOT 94] and references therein). In this survey paper I shall mainly discus...

Quasi-regular topologies for L-resolvents and semi-Dirichlet forms

We prove that for any semi-Dirichlet form (ε, D(ε)) on a measurable Lusin space E there exists a Lusin topology with the given σ-algebra as the Borel σ-algebra so that (ε, D(ε)) becomes quasi–regular. However one has to enlarge E by a zero set. More generally a corresponding result for arbitrary L-resolvents is proven.

Existence and stability of solutions of general semilinear elliptic equations with measure data

Nonlinear degenerate elliptic equations with measure data

In this paper we prove existence results for some nonlinear degenerate elliptic equations with data in the space of bounded Radon measures and we improve the results already obtained in Cirmi G.R., On the existence of solutions to non-linear degenerate elliptic equations with measure data, Ricerche Mat. 42 (1993), no. 2, 315–329.