Elliptic operators and Muckenhoupt weights

TOSCHI, MARISA

Milano

Seminario; Seminar of Calculus of Variations and Differential Equations; 2014

Politecnico di Milano, Dipartamento di Matematica.

Under different conditions on a domain $\Omega$, we prove some weighted a priori estimates for solutions to the Dirichlet problem when the weight is in the Muckenhoupt class $A_p(R^n)$. In particular, we are interested in the case of weights which are powers of the distance to the boundary of $\Omega$ and we study for which powers these weights belongs to $A_p(R^n)$. These results can be extended to a metric measure space $(X;d;\mu)$ satisfying the so called Ahlfors condition, which is a particular case of space of homogeneous type. We also obtain a new family of weights in the class $A_p(X;d;\mu)$ for a general metric measure space.