Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds |
| |
Authors: | Takeshi Isobe |
| |
Institution: | Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan |
| |
Abstract: | We study some basic analytical problems for nonlinear Dirac equations involving critical Sobolev exponents on compact spin manifolds. Their solutions are obtained as critical points of certain strongly indefinite functionals defined on H1/2-spinors with critical growth. We prove the existence of a non-trivial solution for the Brezis-Nirenberg type problem when the dimension m of the manifold is larger than 3. We also prove a global compactness result for the associated Palais-Smale sequences and the regularity of -weak solutions. |
| |
Keywords: | Nonlinear Dirac equations Critical Sobolev exponent Strongly indefinite functional Critical point theory Compactness Regularity |
本文献已被 ScienceDirect 等数据库收录! |