JournalsaihpcVol. 34, No. 5pp. 1075–1129

Boundary-degenerate elliptic operators and Hölder continuity for solutions to variational equations and inequalities

  • Paul M.N. Feehan

    Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, United States

  • Camelia A. Pop

    School of Mathematics, University of Minnesota, Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, United States
Boundary-degenerate elliptic operators and Hölder continuity for solutions to variational equations and inequalities cover
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Abstract

We prove local supremum bounds, a Harnack inequality, Hölder continuity up to the boundary, and a strong maximum principle for solutions to a variational equation defined by an elliptic operator which becomes degenerate along a portion of the domain boundary and where no boundary condition is prescribed, regardless of the sign of the Fichera function. In addition, we prove Hölder continuity up to the boundary for solutions to variational inequalities defined by this boundary-degenerate elliptic operator.

Cite this article

Paul M.N. Feehan, Camelia A. Pop, Boundary-degenerate elliptic operators and Hölder continuity for solutions to variational equations and inequalities. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 5, pp. 1075–1129

DOI 10.1016/J.ANIHPC.2016.07.005