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Infinite-dimensional elliptic equations with Hölder-continuous coefficients. (English) Zbl 0926.35153

Summary: Infinite-dimensional elliptic equations \[ \mu u(x)-\textstyle{{1\over 2}}\text{ Tr}[Q(x) D^2u(x)]= f(x),\quad x\in H \] with Hölder-continuous coefficients are here studied by purely analytic methods. In particular, Schauder estimates for solutions of such equations are derived.

MSC:

35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
47D03 Groups and semigroups of linear operators
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
46G12 Measures and integration on abstract linear spaces
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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