Existence, uniqueness and optimal regularity results for very weak solutions to nonlinear elliptic systems
- Prelegent(ci)
- Sebastian Schwarzacher
- Termin
- 15 października 2015 12:30
- Pokój
- p. 4060
- Seminarium
- Seminarium Zakładu Równań Fizyki Matematycznej
Abstract. We establish existence, uniqueness and optimal regularity results for very weak
solutions to certain nonlinear elliptic boundary value problems. We introduce structural
asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are su cient and in
many cases also necessary for building such a theory. We provide a unified approach that
leads qualitatively to the same theory as that one available for linear elliptic problems with
continuous coe cients, e.g. the Poisson equation. The result is based on several novel tools
that are of independent interest: local and global estimates for (non)linear elliptic systems
in weighted Lebesgue spaces with Muckenhoupt weights, a generalization of the celebrated
div-curl lemma for identification of a weak limit in border line spaces and the introduction
of a Lipschitz approximation that is stable in weighted Sobolev spaces.