Monotonicity formulas for obstacle problems with Lipschitz coefficients | Zendy

Matteo Focardi | Zendy; Maria Stella Gelli | Zendy; Emanuele Spadaro | Zendy

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Monotonicity formulas for obstacle problems with Lipschitz coefficients

Author(s) -

Matteo Focardi,

Maria Stella Gelli,

Emanuele Spadaro

Publication year - 2015

Publication title -

calculus of variations and partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.329

H-Index - 76

eISSN - 1432-0835

pISSN - 0944-2669

DOI - 10.1007/s00526-015-0835-0

Subject(s) - mathematics , monotonic function , lipschitz continuity , obstacle problem , quadratic equation , type (biology) , obstacle , fourier series , term (time) , boundary (topology) , mathematical analysis , pure mathematics , discrete mathematics , geometry , ecology , physics , quantum mechanics , political science , law , biology

We prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a Holder continuous linear term. With the help of those formulas we are able to carry out the full analysis of the regularity of free-boundary points following the approaches by Caffarelli, Monneau and Weiss

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