Singular problems arise in the study of non-Newtonian fluids, boundary layer phenomena for viscous fluids, chemical heterogeneous catalysts, as well as in the theory of heat conduction in electrically conducting materials. An increasing attention to singular stationary or evolution equations has been paid in the last decades. In the present talk we deal with a strongly singular problem in an exterior domain driven by the p-Laplace operator. In particular we prove existence results and discuss decay rates of the solutions at the boundary and at infinity. The unboundedness of the domain as well as the presence of a strong singular term prevent a straightforward application of classical variational methods. Our results are based on approximation scheme and sub-supersolution techniques. The talk is based on the paper M. CHHETRI, F. FARACI, Strongly singular problems in exterior domains, J. Differential Equations 313 (2022) 285--313.
Strongly singular problems in exterior domains*
Francesca Faraci, University of Catania, ItalyAuthors: Maya Chhetri, Francesca Faraci
2022 AWM Research Symposium
Advances in Nonlinear Partial Differential Equations