Fine Regularity of solutions to the Dirichlet Problem associated with the Regional Fractional Laplacian
Received:November 19, 2019  Revised:January 14, 2020
Key Word: Regional fractional Laplacian   Dirichlet problem   H&  #246  lder Regularity  
Fund ProjectL:The Science and Technology Research Program of Higher Educational in Bebei Province
Author NameAffiliationE-mail
Yanyan Li Shijiazhuang Tiedao University liyanyan425@yahoo.com 
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Abstract:
      In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian on a bounded open set with C^1,1 boundary. We prove that the inhomogenous Dirichlet problem admits a unique weak, under a certain condition. To solve this problem, we consider it into two special cases. Finally, take into account the preceding two cases, we obtain the general result.
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