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Browsing by Subject "regularity theory"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Double phase problems: a survey of some recent results
    (Wydawnictwa AGH, 2022) Papageorgiou, Nikolaos Socrates
    We review some recent results on double phase problems. We focus on the relevant function space framework, which is provided by the generalized Orlicz spaces. We also describe the basic tools and methods used to deal with double phase problems, given that there is no global regularity theory for these problems.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions
    (Wydawnictwa AGH, 2023) Bahja, Hamid El
    We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard $p(x,t),q(x,t)$-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time $L^{\infty}$ bounds for the weak solutions.