Leírás
We kindly invite you to the Farkas Miklós Seminar.
19 September (Thursday) 10.15-11.15, BME, H306
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Csaba Farkas (Sapientia - Hungarian University of Transylvania, Department of Mathematics-Informatics)
Compact Sobolev embeddings on non-compact manifolds with applications
In this talk, we collect recent achievements obtained in the theory of geometric analysis, by exploiting elements from the calculus of variations, partial differential equations, Riemann-Finsler geometry and group theory. First, for a given complete non-compact Riemannian manifold (M, g) with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries G of (M, g) that characterizes the coerciveness of G in the sense of Skrzypczak and Tintarev (Arch Math 101(3): 259--268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). Then we give some applications for such results, first, we investigate the existence of multiple solutions for a low-dimensional Dirichlet eigenvalue problem with non-standard growth on a Randers space. Variational techniques, depending in particular on a minimax theorem and the previous compact embeddings, are employed to establish the existence of multiple group invariant solutions. After that, we deal with a quasilinear elliptic equation involving a critical Sobolev exponent on non-compact Randers spaces. Under very general assumptions on the perturbation, we prove the existence of a non-trivial solution. The approach is based on the direct methods of the calculus of variations. We end this talk with the multiplicity of singular fourth-order Schrödinger equation on Hadamard manifolds.
The organizers
(István Faragó, János Karátson, Róbert Horváth, Miklós Mincsovics, Gabriella Svantnerné Sebestyén)
Visit the homepage of the seminar: http://math.bme.hu/farkas_seminar