TY - JOUR
T1 - On the location of concentration points for singularly perturbed elliptic equations
AU - Secchi, S.
AU - Squassina, Marco
PY - 2004
Y1 - 2004
N2 - By exploiting a variational identity of Pohozaev-Pucci-Serrin\r\ntype for solutions of class C1, we get some necessary conditions for\r\nlocating the peak-points of a class of singularly perturbed quasilinear\r\nelliptic problems in divergence form. More precisely, we show that the\r\npoints where the concentration occurs, in general, must belong to what\r\nwe call the set of weak-concentration points. Finally, in the semilinear\r\ncase, we provide a new necessary condition which involves the Clarke\r\nsubdifferential of the ground-state function.
AB - By exploiting a variational identity of Pohozaev-Pucci-Serrin\r\ntype for solutions of class C1, we get some necessary conditions for\r\nlocating the peak-points of a class of singularly perturbed quasilinear\r\nelliptic problems in divergence form. More precisely, we show that the\r\npoints where the concentration occurs, in general, must belong to what\r\nwe call the set of weak-concentration points. Finally, in the semilinear\r\ncase, we provide a new necessary condition which involves the Clarke\r\nsubdifferential of the ground-state function.
KW - spike location
KW - spike location
UR - https://publicatt.unicatt.it/handle/10807/91319
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=44049098911&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=44049098911&origin=inward
M3 - Article
SN - 1079-9389
VL - 9
SP - 53
EP - 71
JO - Advances in Differential Equations
JF - Advances in Differential Equations
IS - N/A
ER -