Results 141 to 150 of about 425 (156)

Hypoellipticity of Nonlinear Second Order Partial Differential Equations

Journal of Partial Differential Equations, 1988
Let \(u\in C^{\rho}_{loc}(\Omega)\), \(\rho >4\), be a solution of a smooth nonlinear p.d.e. \(F(x,u,\partial u,\partial^ 2u)=0.\) It is proved in this paper that, if the principal symbol of the linearized operator at u is non negative and satisfies the so-called Hörmander condition, then \(u\in C^{\infty}(\Omega).\) The main tool used in the proof is ...
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Stochastic Differential Equations and Hypoelliptic Operators

2004
The first half of the twentieth century saw some remarkable developments in analytic probability theory. Wiener constructed a rigorous mathematical model of Brownian motion. Kolmogorov discovered that the transition probabilities of a diffusion process define a fundamental solution to an associated heat equation.
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Hypoellipticity of Anisotropic Partial Differential Equations

2014
We propose an approach based on methods from microlocal analysis, for characterizing the hypoellipticity in C°° and Gevrey classes of semilinear anisotropic partial differential operators with multiple characteristics, in dimension n > 3.
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The method of stochastic characteristics for linear second-order hypoelliptic equations

Probability Surveys, 2023
Juraj Foldes, David P Herzog
exaly  

Estimation of higher derivatives of the solutions for a class of almost hypoelliptic equations in an infinite strip

Journal of Contemporary Mathematical Analysis, 2010
V N Margaryan, Margaryan V N
exaly  

On smooth solutions of a class of almost hypoelliptic equations

Journal of Contemporary Mathematical Analysis, 2013
H G Ghazaryan, Ghazaryan H G
exaly  

The hypoelliptic Robin problem for quasilinear elliptic equations

Discrete and Continuous Dynamical Systems - Series S, 2020
Kazuaki Taira
exaly  

On integrable with a weight solutions of a class of almost hypoelliptic equations

Journal of Contemporary Mathematical Analysis, 2016
V N Margaryan, Margaryan V N
exaly  

Hypoelliptic Convolution Equations in the Space of Distributions on Noncompact Semi-Simple Lie Groups

Rocky Mountain Journal of Mathematics, 2009
Khalifa Trimeche
exaly  

Correct Solvability of the Dirichlet Problem in the Half-space for Regular Hypoelliptic Equations

Journal of Contemporary Mathematical Analysis, 2019
G A Karapetyan, Karapetyan G A
exaly