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Construction --- Elements finis, methode des --- Equation de la chaleur

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"In this Memoir we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain our ideas and for completeness, we also review the constant rank theorem technique for the spacetime Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function"--

Heat equation. --- Space and time. --- Équation de la chaleur. --- Espace et temps. --- Heat equation --- Équation de la chaleur --- Numerical solutions. --- Solutions numériques --- Numerical analysis --- Numerical solutions

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Functional analysis --- Heat equation --- Singular integrals --- Intégrales singulières --- Équation de la chaleur --- Integrals, Singular --- Integral operators --- Integral transforms --- Diffusion equation --- Heat flow equation --- Differential equations, Parabolic --- Intégrales singulières. --- Équation de la chaleur.

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Heat equation. --- Équation de la chaleur. --- Equations aux derivees partielles paraboliques --- Equations aux derivees partielles --- Methodes hilbertiennes

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Calculus of variations. --- Differential equations, Partial. --- Heat equation. --- Calcul des variations. --- Équations aux dérivées partielles. --- Équation de la chaleur. --- Differential calculus. --- Differential equations, Parabolic. --- Curvature.