Results 11 to 20 of about 1,955 (98)

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
wiley   +1 more source

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

New Results About the Lambda Constant and Ground States of the 𝑊-Functional

Advanced Nonlinear Studies, 2020
In this paper, we study properties of the lambda constants and the existence of ground states of Perelman’s famous W-functional from a variational formulation. We have two kinds of results.
Ma Li
doaj   +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

Notes on continuity result for conformable diffusion equation on the sphere: The linear case

Demonstratio Mathematica, 2022
In this article, we are interested in the linear conformable diffusion equation on the sphere. Our main goal is to establish some results on the continuity problem with respect to fractional order.
Nguyen Van Tien
doaj   +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

Results on existence for generalized nD Navier-Stokes equations

Open Mathematics, 2019
In this paper we consider a class of nD Navier-Stokes equations of Kirchhoff type and prove the global existence of solutions by using a new approach introduced in [Jday R., Zennir Kh., Georgiev S.G., Existence and smoothness for new class of n ...
Zennir Khaled
doaj   +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
wiley   +1 more source

Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems [PDF]

, 2018
We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal criteria for ...
Beck, Lisa, Mingione, Giuseppe
core   +2 more sources