Maximal Sobolev regularity in Neumann problems for gradient systems in\n infinite dimensional domains

2013/09/25 by Giuseppe Da Prato, Da Prato, Giuseppe, Alessandra Lunardi +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1309.6519

openalex publication_date 2013/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an elliptic Kolmogorov equation lambda u - Ku =f in a convex\nsubset C of a separable Hilbert space X. We prove maximal Sobolev regularity of\nits weak solution, when lambda >0 and f is in L²(C,nu), where nu is the\nlog-concave measure associated to the system. Moreover we prove maximal\nestimates on the gradient of u, that allow to show that u satisfies the Neumann\nboundary condition in the sense of traces at the boundary of C. The general\nresults are applied to Kolmogorov equations of reaction-diffusion stochastic\nPDEs and Cahn-Hilliard stochastic PDEs in convex sets of suitable Hilbert\nspaces.\n

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