Elliptic problems with a parameter in unbounded domains. (English) Zbl 1180.35215

Authors’ abstract: Linear elliptic boundary-value problems with a parameter are studied. The Agranovich-Vishik method and specially introduced function spaces allow us to consider mixed-order problems in unbounded domains. We obtain a priori estimates and unique solvability for large values of the parameter. These results are used to study analytic semigroups and the Fredholm property of general elliptic problems in unbounded domains.


35J47 Second-order elliptic systems
35J57 Boundary value problems for second-order elliptic systems
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B45 A priori estimates in context of PDEs