Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton–Jacobi equations

Consider the diffusive Hamilton–Jacobi equation u t - Δ u = | ∇ u | p + h ( x ) in Ω × ( 0 , T ) with Dirichlet conditions, which arises in stochastic control problems as well as in KPZ type models. We study the question of the gradient blowup rate for classical solutions with  p > 2 . We first c...

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Veröffentlicht in:	Calculus of variations and partial differential equations 2020-10, Vol.59 (5), Article 153
Hauptverfasser:	Attouchi, Amal, Souplet, Philippe
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Analysis of PDEs Calculus of Variations and Optimal Control Optimization Control Dirichlet problem Domains Mathematical and Computational Physics Mathematics Mathematics and Statistics Optimal control Questions Stochastic processes Systems Theory Theoretical
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