Geodesic
Boundary-degenerate elliptic operators and Hölder continuity for solutions to variational equations and inequalities
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1075-1129

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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.

DOI : 10.1016/j.anihpc.2016.07.005
Classification : 35J70, 35J86, 49J40, 35R45, 35R35, 49J20, 60J60
Keywords: Degenerate elliptic differential operator, Degenerate diffusion process, Harnack inequality, Hölder continuity, Variational inequality, Weighted Sobolev space 
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     author = {Feehan, Paul M.N. and Pop, Camelia A.},
     title = {Boundary-degenerate elliptic operators and {H\"older} continuity for solutions to variational equations and inequalities},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1075--1129},
     publisher = {Elsevier},
     volume = {34},
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     doi = {10.1016/j.anihpc.2016.07.005},
     zbl = {1386.35114},
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Feehan, Paul M.N.; Pop, Camelia A. Boundary-degenerate elliptic operators and Hölder continuity for solutions to variational equations and inequalities. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1075-1129. doi: 10.1016/j.anihpc.2016.07.005

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