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A maximum principle and related problems for a Laplacian in Hilbert space. (English) Zbl 0885.35142
Summary: We establish a maximum principle for a Laplace operator in a Hilbert space and as a result, obtain an extension of the Laplace operator in Hilbert space defined in our previous paper [World Sci. Ser. Appl. Anal. 1, 431-440 (1992; Zbl 0829.47037)]. The related Dirichlet and Poisson problems are also discussed.

MSC:
35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
35B50 Maximum principles in context of PDEs
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