Local Elliptic Regularity for the Dirichlet Fractional Laplacian
Local Elliptic Regularity for the Dirichlet Fractional Laplacian
Abstract We prove the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>W</m:mi> <m:mi>loc</m:mi> <m:mrow> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>s</m:mi> </m:mrow> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> </m:math> ${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℝ</m:mi> <m:mi>N</m:mi> </m:msup> </m:math> …