We consider the supercritical problem -Delta u = vertical bar u vertical bar(p-2)u in Omega, u = 0 on partial derivative Omega, where Omega is a bounded smooth domain in R-N and p smaller than the critical exponent 2(N,k)* := 2(N-k)/N-k-2 for the Sobolev embedding of H-1(RN-k) in L-q(RN-k), 1 <= k <= N - 3. We show that in some suitable domains Omega there are positive and sign changing solutions with positive and negative layers which concentrate along one or several k-dimensional submanifolds of partial derivative Omega as p approaches 2(N,k)* from below. (C) 2013 Elsevier Inc. All rights reserved.
Boundary clustered layers near the higher critical exponents / Nils, Ackermann; Monica, Clapp; Pistoia, Angela. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 254:10(2013), pp. 4168-4193. [10.1016/j.jde.2013.02.015]
Boundary clustered layers near the higher critical exponents
PISTOIA, Angela
2013
Abstract
We consider the supercritical problem -Delta u = vertical bar u vertical bar(p-2)u in Omega, u = 0 on partial derivative Omega, where Omega is a bounded smooth domain in R-N and p smaller than the critical exponent 2(N,k)* := 2(N-k)/N-k-2 for the Sobolev embedding of H-1(RN-k) in L-q(RN-k), 1 <= k <= N - 3. We show that in some suitable domains Omega there are positive and sign changing solutions with positive and negative layers which concentrate along one or several k-dimensional submanifolds of partial derivative Omega as p approaches 2(N,k)* from below. (C) 2013 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
