An extension of Hörmander's hypoellipticity theorem

DOI10.1007/s11118-014-9439-0zbMath1317.35091arXiv1312.3557OpenAlexW2071884610MaRDI QIDQ2256551

Nathan Totz, David P. Herzog

Publication date: 19 February 2015

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.3557

zbMATH Keywords

Malliavin calculushypoellipticitypseudo-differential calculusHörmander's theoremdegenerate stochastic differential equations

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate elliptic equations (35J70) Stochastic calculus of variations and the Malliavin calculus (60H07) Hypoelliptic equations (35H10) Subelliptic equations (35H20)

Cites Work

• Theory of Bessel potentials. I
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Smooth densities for solutions to stochastic differential equations with jumps
• Stochastic calculus of variations for stochastic partial differential equations
• Commutateurs d'intégrales singulières et opérateurs multilinéaires
• Hölder estimates for subelliptic operators
• Balls defined by nonsmooth vector fields and the Poincaré inequality.
• Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
• Hypoelliptic second order differential equations
• Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality
• Partial Differential Equations for Probabilists
• Non-divergence equations structured on Hörmander vector fields: heat kernels and Harnack inequalities
• Commutator estimates and the euler and navier-stokes equations
• [https://portal.mardi4nfdi.de/wiki/Publication:3889862 Martingales, the Malliavin calculus and hypoellipticity under general H�rmander's conditions]
• Weighted Sobolev-Poincare Inequalities and Pointwise Estimates for a Class of Degenerate Elliptic Equations
• Hölder continuity of weak solutions to subelliptic equations with rough coefficients
• Malliavin Calculus with Applications to Stochastic Partial Differential Equations
• Nonsmooth Hörmander vector fields and their control balls
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