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2015-02-24 Nonlinear Seminar

dr Jacek Gulgowski
Compactness in spaces of functions of bounded variation.

The studies on the existence of fixed points of mappings in Banach spaces often involve methods connected with the Schauder fixed point theorem or the Leray-Schauder degree. Both approaches require the considered mappings to be completely continuous, and therefore, if one wants to work in spaces of functions of bounded variation, it is crucial to understand the mutual relations between $$ \Lambda BV(I) $$ and $$ BV_\phi(I) $$ spaces. During the seminar we are going to discuss certain results on compact embeddings of such spaces and characterise the complete continuity of some nonlinear integral operators acting in $$ BV_p(I) $$ spaces.