Results 91 to 100 of about 125 (115)

Smoothness of solutions of almost hypoelliptic equations

Journal of Contemporary Mathematical Analysis, 2008
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V N Margaryan, H G Ghazaryan, Margaryan V N   +2 more
exaly   +2 more sources

On Solvability of Regular Hypoelliptic Equations in ℝn

Journal of Contemporary Mathematical Analysis, 2018
In this paper the unique solvability of regular hypoelliptic equations in multianisotropic weighted functional spaces is proved by means of special integral representation of functions through a regular operator. The existence of the solutions is proved by constructing approximate solutions using multianisotropic integral operators.
G A Karapetyan, Karapetyan G A
exaly   +2 more sources

Smoothness of solutions of almost hypoelliptic equations

Journal of Contemporary Mathematical Analysis, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +3 more sources

Gradient Estimates for Some Semi-Linear Hypoelliptic Equations

Acta Applicandae Mathematicae, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bin Qian, Qian Bin
exaly   +3 more sources

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

ON THE FUNCTIONAL DIMENSION OF THE SOLUTION SPACE OF HYPOELLIPTIC EQUATIONS

Mathematics of the USSR-Sbornik, 1982
Translation from Mat. Sb., Nov. Ser. 115(157), No.4, 614-631 (Russian) (1981; Zbl 0489.35031).
Margaryan, V. N., Kazaryan, G. G.
openaire   +1 more source

Hypoellipticity of Nonlinear Partial Differential Equations

Journal of Partial Differential Equations, 1994
Summary: We study the hypoellipticity problems for fully nonlinear partial differential equations of order \(m\). For a solution \(u \in C^ \rho_{\text{loc}} (\Omega)\), if the linearized operator on \(u\) satisfies some subelliptic conditions, we can deduce \(u \in C^ \infty (\Omega)\) by using the paradifferential operator theory of J.-M. Bony.
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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

An Invariant Harnack Inequality for a Class of Hypoelliptic Ultraparabolic Equations

Mediterranean Journal of Mathematics, 2004
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KOGOJ, ALESSIA ELISABETTA, Lanconelli, Ermano   +1 more
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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 ...
openaire   +2 more sources