Extension in generalized Orlicz-Sobolev spaces

Abstract

<p>We study the existence of an extension operator Lambda: W1,phi(S2) -> W1,psi(Rn). We assume that cp is an element of Phi w(S2) has generalized Orlicz growth, 0 is an element of Phi w(Rn) is an extension of cp, and that S2 subset of Rn is an (e, 5)-domain. Special cases include the classical constant exponent case, the Orlicz case, the variable exponent case, and the double phase case.<br></p><p>(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).</p>