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## Abstract Let __u__ be a weak solution of the equation (-Δ)^__m__^ __u__ = __f__ with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ R^__n__^. In this paper, we obtain some estimates for the Green's function associated to this problem. Moreover, under appropriate conditions on __p__, we prove some weighted Sobolev a priori estimates for the solution __u__, where the weight is a power of the distance function. This result extends previous work by R. G. Durán and M. Sanmartino ([Indiana Univ. Math. J. 57 (2008), no. 7, 3463–3478] and [Anal. Theory Appl. 26 (2010), no. 4, 339–349]).

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Author

Marisa Toschi

Publisher

Walter de Gruyter GmbH

Published

2015

Language

EN

Field

Mathematics (Physical Sciences)