Results 11 to 20 of about 1,664 (104)
LOCALIZATION FOR THE TORSION FUNCTION AND THE STRONG HARDY INEQUALITY
Mathematika, Volume 67, Issue 2, Page 514-531, April 2021., 2021 Abstract Two‐sided bounds for the efficiency of the torsion function are obtained in terms of the square of the distance to the boundary function under the hypothesis that the Dirichlet Laplacian satisfies a strong Hardy inequality. Localization properties of the torsion function are obtained under that hypothesis. An example is analyzed in detail.
M. van den Berg, T. Kappeler
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Sign changing solutions of Poisson's equation
Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 513-536, September 2020., 2020 Abstract Let Ω be an open, possibly unbounded, set in Euclidean space Rm with boundary ∂Ω, let A be a measurable subset of Ω with measure |A| and let γ∈(0,1). We investigate whether the solution vΩ,A,γ of −Δv=γ1Ω∖A−(1−γ)1A with v=0 on ∂Ω changes sign. Bounds are obtained for |A| in terms of geometric characteristics of Ω (bottom of the spectrum of the ...
M. van den Berg, D. Bucur
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The Dirichlet Problem for elliptic equations in unbounded domains of the plane
Journal of Function Spaces, Volume 6, Issue 1, Page 47-58, 2008., 2008 In this paper we prove a uniqueness and existence theorem for the Dirichlet problem in W2,p for second order linear elliptic equations in unbounded domains of the plane. Here the leading coefficients are locally of class VMO and satisfy a suitable condition at infinity.
Paola Cavaliere +2 more
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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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Examples of non-Dini domains with large singular sets
Advanced Nonlinear Studies, 2023 Let uu be a nontrivial harmonic function in a domain D⊂RdD\subset {{\mathbb{R}}}^{d}, which vanishes on an open set of the boundary. In a recent article, we showed that if DD is a C1{C}^{1}-Dini domain, then, within the open set, the singular set of uu ...
Kenig Carlos, Zhao Zihui
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Stagnation zones of ideal flows in long and narrow bands
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 62, Page 3339-3356, 2004., 2004 We investigate stagnation zones of flows of ideal incompressible fluid in narrow and long bands. With the bandwidth being much less than its length, these flows are almost stationary over large subdomains, where their potential functions are almost constant. These subdomains are called s‐zones. We estimate the size and the location of these s‐zones.
V. M. Miklyukov +2 more
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Multiplicity of concentrating solutions for a class of magnetic Schrödinger-Poisson type equation
Advances in Nonlinear Analysis, 2020 In this paper, we study the following nonlinear magnetic Schrödinger-Poisson type ...
Liu Yueli, Li Xu, Ji Chao
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Capillary Schwarz symmetrization in the half-space
Advanced Nonlinear Studies, 2023 In this article, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space.
Lu Zheng, Xia Chao, Zhang Xuwen
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On the location of two blow up points on an annulus for the mean field equation [PDF]
, 2014 We consider the mean field equation on two-dimensional annular domains, and prove that if $P$ and $Q$ are two blow up points of a blowing-up solution sequence of the equation, then we must have $P=-Q$.Comment: To appear in ...
Grossi, M., Takahashi, F.
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The Poisson equation in homogeneous Sobolev spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 36, Page 1909-1921, 2004., 2004 We consider Poisson′s equation in an n‐dimensional exterior domain G(n ≥ 2) with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certain Lq(G)‐spaces there exists a solution in the homogeneous Sobolev space S2,q(G), containing functions being local in Lq(G) and having second‐order derivatives in Lq(G ...
Tatiana Samrowski, Werner Varnhorn
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