LIPSCHITZ REGULARITY RESULTS FOR NONLINEAR STRICTLY ELLIPTIC EQUATIONS AND APPLICATIONS

Abstract : Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.
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Journal of Differential Equations, Elsevier, 2017, <10.1016/j.jde.2017.05.020>
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Dernière modification le : mercredi 12 juillet 2017 - 01:15:56
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Olivier Ley, Vinh Duc Nguyen. LIPSCHITZ REGULARITY RESULTS FOR NONLINEAR STRICTLY ELLIPTIC EQUATIONS AND APPLICATIONS. Journal of Differential Equations, Elsevier, 2017, <10.1016/j.jde.2017.05.020>. <hal-01344438>

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