Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces

DOI10.1090/S0002-9947-05-03638-XzbMath1131.35008OpenAlexW1988232098MaRDI QIDQ5313317

Richard F. Bass, Siva R. Athreya, Edwin A. Perkins

Publication date: 29 August 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03638-x

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Second-order elliptic equations (35J15) Transition functions, generators and resolvents (60J35) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (11)

Time regularity for generalized Mehler semigroups ⋮ Schauder regularity results in separable Hilbert spaces ⋮ A counterexample to \(L^{\infty}\)-gradient type estimates for Ornstein-Uhlenbeck operators ⋮ Schauder estimates for elliptic equations in Banach spaces associated with stochastic reaction-diffusion equations ⋮ Analytic semigroups and some degenerate evolution equations defined on domains with corners ⋮ Directed chain stochastic differential equations ⋮ Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type ⋮ Schauder theorems for Ornstein-Uhlenbeck equations in infinite dimension ⋮ Degenerate stochastic differential equations for catalytic branching networks ⋮ An optimal regularity result for Kolmogorov equations and weak uniqueness for some critical SPDEs ⋮ Schauder theorems for a class of (pseudo‐)differential operators on finite‐ and infinite‐dimensional state spaces

Cites Work

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• Ecole d'été de probabilités de Saint-Flour XII - 1982
• Some results on elliptic and parabolic equations in Hilbert spaces
• An interpolation method to characterize domains of generators of semigroups
• Infinite-dimensional elliptic equations with Hölder-continuous coefficients
• Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type
• Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains

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