Let (M, g) and be two Riemannian manifolds of dimensions m and k, respectively. Let . The warped product is the (m + k)-dimensional product manifold furnished with metric . We prove that the supercritical problem has a solution concentrated along a k-dimensional minimal submanifold of as the real parameter goes to zero, provided the function h and the sectional curvatures along satisfy a suitable condition.
Blow-up solutions concentrated along minimal submanifolds for some supercritical elliptic problems on Riemannian manifolds / Marco, Ghimenti; Anna Maria, Micheletti; Pistoia, Angela. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - STAMPA. - 14:2(2013), pp. 503-525. [10.1007/s11784-014-0168-1]
Blow-up solutions concentrated along minimal submanifolds for some supercritical elliptic problems on Riemannian manifolds
PISTOIA, Angela
2013
Abstract
Let (M, g) and be two Riemannian manifolds of dimensions m and k, respectively. Let . The warped product is the (m + k)-dimensional product manifold furnished with metric . We prove that the supercritical problem has a solution concentrated along a k-dimensional minimal submanifold of as the real parameter goes to zero, provided the function h and the sectional curvatures along satisfy a suitable condition.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.