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math.NA2015★ 242 cited
A fractional Laplace equation: regularity of solutions and Finite Element approximations
Gabriel Acosta, Juan Pablo Borthagaray
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are…
math.AP2015
A mass transportation approach for Sobolev inequalities in variable exponent spaces
Juan Pablo Borthagaray, Julián Fernández Bonder, Analía Silva
In this paper we provide a proof of the Sobolev-Poincaré inequality for variable exponent spaces by means of mass transportation methods. The importance of this approach is that th…