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arXiv · 1309.6519

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

Giuseppe Da Prato·Alessandra Lunardi
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Abstract

We consider an elliptic Kolmogorov equation lambda u - Ku =f in a convex subset C of a separable Hilbert space X. We prove maximal Sobolev regularity of its weak solution, when lambda >0 and f is in L^2(C,nu), where nu is the log-concave measure associated to the system. Moreover we prove maximal estimates on the gradient of u, that allow to show that u satisfies the Neumann boundary condition in the sense of traces at the boundary of C. The general results are applied to Kolmogorov equations of reaction-diffusion stochastic PDEs and Cahn-Hilliard stochastic PDEs in convex sets of suitable Hilbert spaces.

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Giuseppe Da Prato, Alessandra Lunardi. 2013-09-25. Maximal Sobolev regularity in Neumann problems for gradient systems in infinite dimensional domains. https://arxiv.org/abs/1309.6519

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