A Hölder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions

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In this article we present the existence, uniqueness, and Hölder regularity of solutions for the non-local elliptic equations of the type (Formula presented.) where (Formula presented.) Here χ(y) is a suitable indicator function, J(y)dy is a rotationally invariant Lévy measure on ℝd (Formula presented.), and a(y) is an only measurable function with positive lower and upper bounds.

Original languageEnglish
Pages (from-to)653-673
Number of pages21
JournalPotential Analysis
Issue number4
Publication statusPublished - 2015 Nov 1



  • Hölder estimates
  • Integro-differential equations
  • Non-local elliptic equations
  • Non-symmetric measurable kernels
  • Subordinate Brownian motion

ASJC Scopus subject areas

  • Analysis

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