Sobolev inequalities in arbitrary domains
2016 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 293, 644-696 p.Article in journal (Refereed) PublishedText
A theory of Sobolev inequalities in arbitrary open sets in R-n is established. Boundary regularity of domains is replaced with information on boundary traces of trial functions and of their derivatives up to some explicit minimal order. The relevant Sobolev inequalities exhibit the same critical exponents as in the classical framework. Moreover, they involve constants independent of the geometry of the domain, and hence yield genuinely new results even in the case when just smooth domains are considered. Our approach relies upon new representation formulas for Sobolev functions, and on ensuing pointwise estimates which hold in any open set. (C) 2016 Elsevier Inc. All rights reserved.
Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2016. Vol. 293, 644-696 p.
Sobolev inequalities; Irregular domains; Boundary traces; Optimal norms; Representation formulas
IdentifiersURN: urn:nbn:se:liu:diva-127410DOI: 10.1016/j.aim.2016.02.012ISI: 000373093200014OAI: oai:DiVA.org:liu-127410DiVA: diva2:925589
Funding Agencies|Research Project of Italian Ministry of University and Research (MIUR) Prin [2012TC7588]; GNAMPA of the Italian INdAM (National Institute of High Mathematics)2016-05-022016-04-262016-05-02