Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation in simply-connected domains

New examples of domains with small prescribed volume that are critical points for the first eigenvalue of the Dirichlet Laplace-Beltrami operator are built in [28], under the

Sicbaldi in [16], a new phenomena appears: there are two types of extremal domains, those that are the complement of a small perturbed geodesic ball centered at a nondegenerate

This is the reason why we presented here some new results on the general theory of the existence, uniqueness and regularity of solutions of the strongly damped Schr¨odinger

Druet [1] has proved that for small volumes (i.e. τ > 0 small), the solutions of the isoperimetric problem are close (in a sense to be made precise) to geodesic spheres of

This is the reason why we presented here some new results on the general theory of the existence, uniqueness and regularity of solutions of the strongly damped Schr¨ odinger

In Section 2 are collected results on potential operators (similar to the famous Bogovsk˘ıi op- erator),the Stokes operators with Dirichlet boundary conditions and Hodge

Such new domains have small volume and are close to geodesic balls centered at a nondegenerate critical point of the scalar curvature of the manifold (the existence of at least

7 Solution of the Dirichlet problem for the conjugated Beltrami equation 12 A Appendix: Proof of the properties of some operators 12 B Appendix: Proof of some properties of functions