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- W2090206169 abstract "The starting point of this work is a paper by Alvarez, Lasry and Lions (1997) concerning the convexity and the partial convexity of solutions of fully nonlinear degenerate elliptic equations. We extend their results in two directions. First, we deal with possibly sublinear (but epi-pointed) solutions instead of 1-coercive ones; secondly, the partial convexity of C 2 solutions is extended to the class of continuous viscosity solutions. A third contribution of this paper concerns C 1 , 1 estimates for convex viscosity solutions of strictly elliptic nonlinear equations. To finish with, all the tools and techniques introduced here permit us to give a new proof of the Alexandroff estimate obtained by Trudinger (1988) and Caffarelli (1989). Le point de départ de cet article est un résultat d'Alvarez, Lasry et Lions (1997) sur la convexité et la convexité partielle de solutions d'équations elliptiques dégénérées complètement non linéaires. Nous étendons leurs résultats de deux façons. D'une part, nous pouvons traiter le cas de solutions non nécessairement 1-coercitives, éventuellement sous linéaires (mais épi-pointées) ; d'autre part, la convexité partielle de solutions C 2 est étendue aux solutions de viscosité simplement continues. Une troisième contribution de cet article sont des estimations C 1 , 1 pour les solutions de viscosité convexes des équations non linéaires strictement elliptiques ; pour finir, les outils et techniques de cet article nous permettent de donner une nouvelle démonstration de l'estimation d'Alexandroff, adaptée par Trudinger (1988) et Caffarelli (1989) aux équations elliptiques complètement non linéaires." @default.
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- W2090206169 date "2006-06-01" @default.
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- W2090206169 title "Convexity of solutions and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> estimates for fully nonlinear elliptic equations" @default.
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- W2090206169 doi "https://doi.org/10.1016/j.matpur.2006.01.003" @default.
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