Results 11 to 20 of about 140 (107)
Abstract and Applied AnalysisMSC2020 Classification: 35R11, 35B06 ...
Yu-Cheng An, Guai-Qi Tian
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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
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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
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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
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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
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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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Advances in Nonlinear Analysis, 2020 We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group.
Wang Jialin +3 more
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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
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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
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