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The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary

Autor
Ros, X.; Serra, J.
Tipus d'activitat
Article en revista
Revista
Journal de mathématiques pures et appliquées
Data de publicació
2014-03
Volum
101
Número
3
Pàgina inicial
275
Pàgina final
302
DOI
https://doi.org/10.1016/j.matpur.2013.06.003 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/22795 Obrir en finestra nova
Resum
We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (-d)su=g in O, u=0 in Rn\O, for some s¿(0, 1) and g¿L8(O), then u is Cs(Rn) and u/ds|O is Ca up to the boundary ¿O for some a¿(0, 1), where d(x)=dist(x, ¿O). For this, we develop a fractional analog of the Krylov boundary Harnack method. Moreover, under further regularity assumptions on g we obtain higher order Hölder estimates for u and u/ds. N...
Citació
Ros, X.; Serra, J. The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary. "Journal de mathématiques pures et appliquées", Març 2014, vol. 101, núm. 3, p. 275-302.
Paraules clau
Boundary Regularity, Dirichlet Problem, Fractional Laplacian
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants

  • Ros Oton, Xavier  (autor)
  • Serra Montoli, Joaquim  (autor)