The dirichlet problem has a very long history in mathematics and its importance in partial differential equations harmonic analysis potential theory and the applied sciences is well known in the last decade the dirichlet problem with l2 boundary data has attracted the attention of several mathematicians. In mathematics an elliptic boundary value problem is a special kind of boundary value problem which can be thought of as the stable state of an evolution problemfor example the dirichlet problem for the laplacian gives the eventual distribution of heat in a room several hours after the heating is turned on differential equations describe a large class of natural phenomena from the heat . Question stated roughly consider the dirichlet problem for an elliptic equation on a ball how much can we say about regularity at the boundary of non linear elliptic equations further how can one approach solving a quasi linear or non linear elliptic dirichlet problem with rough data. In this article we consider the analogue of the dirichlet problem for second order elliptic integro differential equations which consists in imposing the boundary conditions in the whole
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