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

Feehan, Paul M.N.; Pop, Camelia A.

doi:10.1016/j.anihpc.2016.07.005

Feehan, Paul M.N. ; Pop, Camelia A.

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1075-1129.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2016.07.005

Classification : 35J70, 35J86, 49J40, 35R45, 35R35, 49J20, 60J60
Mots clés : Degenerate elliptic differential operator, Degenerate diffusion process, Harnack inequality, Hölder continuity, Variational inequality, Weighted Sobolev space

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     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},
     number = {5},
     year = {2017},
     doi = {10.1016/j.anihpc.2016.07.005},
     zbl = {1386.35114},
     mrnumber = {3742516},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.07.005/}
}

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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. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.07.005/

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