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Regularity theory for a class of quasilinear equations
Author(s) -
de Miranda L. H.,
Montenegro M.
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200099
Subject(s) - uniqueness , mathematics , bounded function , norm (philosophy) , class (philosophy) , domain (mathematical analysis) , space (punctuation) , boundary value problem , mathematical analysis , computer science , artificial intelligence , political science , law , operating system
This paper addresses the analysis of the weak solution of − Δ p ω + ω = f in a bounded domain Ω subject to the boundary condition∂ ω ∂ ν = 0on ∂ Ω , when the data f belongs toL 2 ( Ω )and p > 2 . We prove existence and uniqueness of solution for this problem in the Nikolskii spaceN p ′ , 2 p / p ′( Ω ) . Moreover, we obtain energy estimates regarding the Nikolskii norm of ω in terms of theL 2 ( Ω )norm of f .