We prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a H ̈lder 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 developed by Caffarelli, Weiss and Monneau
Monotonicity formulas for obstacle problems with Lipschitz coefficients / M. Focardi; M.S. Gelli; E.N. Spadaro. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 54:(2015), pp. 1547-1573. [10.1007/s00526-015-0835-0]
Monotonicity formulas for obstacle problems with Lipschitz coefficients
FOCARDI, MATTEO;
2015
Abstract
We prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a H ̈lder 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 developed by Caffarelli, Weiss and Monneau
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