Katedra Teorii Optymalizacji i Sterowania

TALK TITLE: Logarithmic double phase problems

ABSTRACT: During the last decade the so-called double phase operator has drawn attention from researchers. Originally it was introduced by Zhikov in the context of homogenization and elasticity theory and as an example for the Lavrentiev phenomenon. It regained popularity after some novel regularity results for local minimizers of the corresponding functional. In this talk I will introduce a double phase type operator with a logarithmic contribution and a class of quasilinear elliptic equations driven by this operator. Furthermore, I will discuss the functional analysis framework needed to study such equations. After that, I consider a problem with superlinear right-hand side and I show, under very general assumptions, a multiplicity result for such problems, whereby I show the existence of a positive solution, a negative one and a solution with changing sign.

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