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On some translation invariant balayage spaces

Walter Hoh, Niels Jacob (1991)

Commentationes Mathematicae Universitatis Carolinae

It is well known that strong Feller semigroups generate balayage spaces provided the set of their excessive functions contains sufficiently many elements. In this note, we give explicit examples of strong Feller semigroups which do generate balayage spaces. Further we want to point out the role of the generator of the semigroup in the related potential theory.

Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data

Alberto Fiorenza, Alain Prignet (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We study the sequence u n , which is solution of - div ( a ( x , 𝔻 u n ) ) + Φ ' ' ( | u n | ) u n = f n + g n in Ω an open bounded set of 𝐑 N and u n = 0 on Ω , when f n tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N -function Φ , and prove a non-existence result.

Orlicz capacities and applications to some existence questions for elliptic pdes having measure data

Alberto Fiorenza, Alain Prignet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the sequence un, which is solution of - div ( a ( x , u n ) ) + Φ ' ' ( | u n | ) u n = f n + g n in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N-function Φ, and prove a non-existence result.

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