Results 1 to 10 of about 191 (141)

Analytic hypoellipticity of Keldysh operators

Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 498-516, November 2021., 2021
Abstract We consider Keldysh‐type operators, P=x1Dx12+a(x)Dx1+Q(x,Dx′), x=(x1,x′) with analytic coefficients, and with Q(x,Dx′) second order, principally real and elliptic in Dx′ for x near zero. We show that if Pu=f, u∈C∞, and f is analytic in a neighbourhood of 0, then u is analytic in a neighbourhood of 0.
Jeffrey Galkowski, Maciej Zworski
wiley   +1 more source

Regularity results for singular elliptic problems

Journal of Function Spaces, Volume 4, Issue 3, Page 243-259, 2006., 2006
Some local and global regularity results for solutions of linear elliptic equations in weighted spaces are proved. Here the leading coefficients are VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a suitable weight function.
Loredana Caso, Miroslav Englis
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Nonanalytic solutions of the KdV equation

Abstract and Applied Analysis, Volume 2004, Issue 6, Page 453-460, 2004., 2004
We construct nonanalytic solutions to the initial value problem for the KdV equation with analytic initial data in both the periodic and the nonperiodic cases.
Peter Byers, A. Alexandrou Himonas
wiley   +1 more source

Which solutions of the third problem for the Poisson equation are bounded?

Abstract and Applied Analysis, Volume 2004, Issue 6, Page 501-510, 2004., 2004
This paper deals with the problem Δu = g on G and ∂u/∂n + uf = L on ∂G. Here, G ⊂ ℝm, m > 2, is a bounded domain with Lyapunov boundary, f is a bounded nonnegative function on the boundary of G, L is a bounded linear functional on W1,2(G) representable by a real measure μ on the boundary of G, and g ∈ L2(G)∩Lp(G), p > m/2.
Dagmar Medková
wiley   +1 more source

Coefficients of singularities of the biharmonic problem of Neumann type: case of the crack

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 5, Page 305-313, 2003., 2003
This paper concerns the biharmonic problem of Neumann type in a sector V. We give a representation of the solution u of the problem in a form of a series u = ∑α∈ECα rα ϕα, and the functions ϕα are solutions of an auxiliary problem obtained by the separation of variables.
Wided Chikouche, Aissa Aibèche
wiley   +1 more source

Integrodifferential equations with analytic semigroups

International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 177-189, 2003., 2003
In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.
D. Bahuguna
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On the strongly damped wave equation and the heat equation with mixed boundary conditions

Abstract and Applied Analysis, Volume 5, Issue 3, Page 175-189, 2000., 2000
We study two one‐dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
Aloisio F. Neves
wiley   +1 more source

Weakly hyperbolic equations with time degeneracy in Sobolev spaces

Abstract and Applied Analysis, Volume 2, Issue 3-4, Page 239-256, 1997., 1997
The theory of nonlinear weakly hyperbolic equations was developed during the last decade in an astonishing way. Today we have a good overview about assumptions which guarantee local well posedness in spaces of smooth functions (C∞, Gevrey). But the situation is completely unclear in the case of Sobolev spaces.
Michael Reissig
wiley   +1 more source

Well‐posedness and regularity results for a dynamic Von Kármán plate

International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 2, Page 237-244, 1995., 1994
We consider the problem of well‐posedness and regularity of solutions for a dynamic von Kármán plate which is clamped along one portion of the boundary and which experiences boundary damping through free edge conditions on the remainder of the boundary.
M. E. Bradley
wiley   +1 more source

Remarks on the existence and decay of the nonlinear beam equation

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 409-412, 1994., 1993
We will consider a class of nonlinear beam equation and we will prove the existence and decay weak ...
Jaime E. Mũnoz Rivera
wiley   +1 more source