A Strong Maximum Principle for the fractional Laplace equation with mixed boundary condition Articles uri icon

publication date

  • November 2021

start page

  • 1699

end page

  • 1715

issue

  • 6

volume

  • 24

International Standard Serial Number (ISSN)

  • 1311-0454

Electronic International Standard Serial Number (EISSN)

  • 1314-2224

abstract

  • In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet;Neumann boundary data which extends the one proved by J. D├ívila (cf. [11]) to the fractional setting. In particular, we present a comparison result for two solutions of the fractional Laplace equation involving the spectral fractional Laplacian endowed with homogeneous mixed boundary condition. This result represents a non–local counterpart to a Hop
    s Lemma for fractional elliptic problems with mixed boundary data







subjects

  • Mathematics

keywords

  • fractional laplacian; maximum principle; mixed boundary conditions