Results 131 to 140 of about 1,209,225 (153)

The regularity of solutions of functional equations and hypoellipticity

1984
In this paper we investigate the regularity of solutions of functional equations of the form $$ \sum\limits_{{j = 1}}^k {aj(x,t)f(hj(x,t))} = F(x,f(x)),...,f({l_s}(x))) + b(x,t) $$ (1.1) where $$ x \in {\mathbb{R}^n},\quad t \in \omega {\mathbb{R}^r},\quad n > 1,\;r \geqslant 1, $$ $$ {h_j}:{\mathbb{R}^n} \times \omega \to \mathbb ...
A. Tsutsumi, Sh. Haruki
openaire   +1 more source

Smoothness of Solutions of Almost Hypoelliptic Equations

Journal of Contemporary Mathematical Analysis, 2009
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A Reflection Principle and an Orthogonal Decomposition Concernig Hypoelliptic Equations

Mathematische Nachrichten, 2002
This paper deals with a jump relation for a boundary integral representation of solutions of hyperelliptic equations which is described by a reflection principle. An orthogonal decomposition of \(L_2\) can be proved by the jump relation. In the orthogonal complement the inhomogeneous adjoint equation has a solution with homogeneous boundary values.
exaly   +3 more sources

An Invariant Harnack Inequality for a Class of Hypoelliptic Ultraparabolic Equations

Mediterranean Journal of Mathematics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
KOGOJ, ALESSIA ELISABETTA, Lanconelli, Ermano   +1 more
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Gradient Estimates for Some Semi-Linear Hypoelliptic Equations

Acta Applicandae Mathematicae, 2012
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Qian, Bin, Chen, Li
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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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Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation Without Angular Cutoff

Communications in Partial Differential Equations, 2012
Yoshinori Morimoto, Nicolas Lerner
exaly  

The Hypoelliptic Robin Problem for Quasilinear Elliptic Equations

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