Communications on Pure and Applied Mathematics · 2001 · 253 citations · 19 references
Natural SciencesMathematicsCritical TheoryDynamical SystemsOptimizationPartial Differential EquationsVariational FormulationVariational InequalitiesVariational PrinciplesWeak FormulationCritical PointsElliptic Partial Differential EquationsExistence Of MinimizersGradient FlowsGround StatesNonlinear Variational FormulationParabolic Partial Differential EquationsVariational Methods In Partial Differential Equations
Abstract By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first‐ and second‐order a priori estimates for the elliptic and parabolic Hessian equations. Our results generalize well‐known results for semilinear elliptic equations and the Monge‐Ampère equation. © 2001 John Wiley & Sons, Inc.
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