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- W2020367011 abstract "We establish the convexity of a viscosity solution of some general second order fully nonlinear elliptic equation with state constraints boundary conditions. Our method combines a comparison principle with the observation that, under suitable assumptions, the convex envelope of the solution is a supersolution. This property relies on the characterization of the viscosity subject of the convex envelope of a lower semicontinuous coercive function. The equation solved by the conjugate of a convex solution as well as partial convexity are topics we also discuss. On établit la convexité de solutions de viscosité d'équations elliptiques du seconda ordre, complètement non linéaires, avec contraintes d'état au bord. Notre méthode repose sur le principe de comparaison et sur l'observation que, sous des hypothèses convenables, l'enveloppe convexe d'une solution est une sursolution. Cette dernière propriété utilise une caractérisation du sous différentiel d'ordre deux (au sens de la théorie des solutions de viscosité) de l'enveloppe convexe d'une fonction coercive, semicontinue inférieurement. Des questions connexes sont traitées, comme la convexité partielle de solutions ou l'équation que doit vérifier la conjuguée d'une fonction convexe." @default.
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- W2020367011 date "1997-03-01" @default.
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- W2020367011 title "Convex viscosity solutions and state constraints" @default.
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- W2020367011 doi "https://doi.org/10.1016/s0021-7824(97)89952-7" @default.
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