Gradient estimates and maximal dissipativity for the Kolmogorov operator in \(\Phi^4_2\)

DOI10.1214/20-ECP294zbMath1434.60151OpenAlexW2993748663MaRDI QIDQ2183147

Giuseppe Da Prato, Arnaud Debussche

Publication date: 26 May 2020

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ecp/1580353227

zbMATH Keywords

gradient estimatesstochastic quantizationKolmogorov operatorsmaximal dissipativity

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) Stochastic quantization (81S20)

Cites Work

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• Estimate for \(P_{t}D\) for the stochastic Burgers equation
• A theory of regularity structures
• Dissipative operators in a Banach space
• \(m\)-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise
• Ergodicity for the 3D stochastic Navier-Stokes equations
• Differentiability of the Feynman-Kac semigroup and a control application
• Strong solutions to the stochastic quantization equations.
• Spectral gap for the stochastic quantization equation on the 2-dimensional torus
• The strong Feller property for singular stochastic PDEs
• An integral inequality for the invariant measure of a stochastic reaction-diffusion equation
• Global well-posedness of the dynamic \(\Phi^{4}\) model in the plane
• Fourier Analysis and Nonlinear Partial Differential Equations
• Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces

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