Differential operators of the first order with degenerate principal symbols

Rainer Felix

Displaying similar documents to “Differential operators of the first order with degenerate principal symbols”

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_{k} : = Δ + \frac{k}{x_{n}} \frac{\partial}{\partial x_{n}}$ on $ℝ^{n}$ is proved. In this note there is shown that in the cases $k \neq 0$ , $k \neq 2$ no other transforms of this kind exist and for case $k = 2$ , all such transforms are described.

Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems

Youssef Akdim, Elhoussine Azroul, Abdelmoujib Benkirane (2003)

Annales mathématiques Blaise Pascal

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An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form $A u + g (x, u, \nabla u)$ , where $A$ is a Leray-Lions operator from $W_{0}^{1, p} (Ω, w)$ into its dual, while $g (x, s, ξ)$ is a nonlinear term which has a growth condition with respect to $ξ$ and no growth with respect to $s$ , but it satisfies a sign condition on $s$ , the second term belongs to $W^{- 1, p^{'}} (Ω, w^{*})$ .

On the solvability of nonlinear elliptic equations in Sobolev spaces

Piotr Fijałkowski (1992)

Annales Polonici Mathematici

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We consider the existence of solutions of the system (*) $P (D) u^{l} = F (x, (\partial^{α} u))$ , l = 1,...,k, $x \in ℝ^{n}$ $(u = (u ¹, . . ., u^{k}))$ in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.

A solution of the Cauchy problem in the class of absolutely continuous distribution-valued functions.

Wiciak, Margareta (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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On some shift invariant integral operators, univariate case

George A. Anastassiou, Heinz H. Gonska (1995)

Annales Polonici Mathematici

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In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving...

A remark on multiresolution analysis of $L^{p} (ℝ^{d})$

Qiyu Sun (1993)

Colloquium Mathematicae

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A condition on a scaling function which generates a multiresolution analysis of $L^{p} (ℝ^{d})$ is given.

The linear symmetric systems associated with the modified Cherednik operators and applications

Hatem Mejjaoli (2012)

Annales mathématiques Blaise Pascal

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We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.

On two classes of weighted Sobolev-Slobodetskiĭ spaces in a dihedral angle

J. Rossmann (1992)

Banach Center Publications

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