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)