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Selected Works of Mariana Smit Vega Garcia
Article
Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift
Annales De L Institut Henri Poincare-analyse Non Lineaire (2017)
  • Nicola Garofalo, University of Padua
  • Arshak Petrosyan, Purdue University
  • Camelia A. Pop, University of Minnesota
  • Mariana Smit Vega Garcia, Fakultät für Mathematik, Universität Duisburg–Essen, 45117 Essen, Germany
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Abstract
We establish the C1+γ -Hölder regularity of the regular free boundary in the stationary obstacle problem defined by the fractional Laplace operator with drift in the subcritical regime. Our method of the proof consists in proving a new monotonicity formula and an epiperimetric inequality. Both tools generalizes the original ideas of G. Weiss in [13] for the classical obstacle problem to the framework of fractional powers of the Laplace operator with drift. Our study continues the earlier research [10], where two of us established the optimal interior regularity of solutions.
Keywords
  • Free boundary
Disciplines
Publication Date
January 5, 2017
DOI
10.1016/j.anihpc.2016.03.001
Citation Information
Nicola Garofalo, Arshak Petrosyan, Camelia A. Pop and Mariana Smit Vega Garcia. "Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift" Annales De L Institut Henri Poincare-analyse Non Lineaire Vol. 34 Iss. 3 (2017) p. 533 - 570
Available at: http://works.bepress.com/mariana-smitvegagarcia/2/