Strong solutions for singular Dirichlet elliptic problems [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We prove an existence result for strong solutions $u\in W^{2,q}\left(\Omega\right) $ of singular semilinear elliptic problems of the form $-\Delta u=g\left( \cdot,u\right) $ in $\Omega,$ $u=\tau$ on $\partial\Omega,$ where ...
Tomas Godoy
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SPECTRAL PROBLEMS FOR THREE-DIMENSIONAL ELLIPTIC EQUATIONS WITH SINGULAR COEFFICIENTS [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2017 The eigenvalues and eigenfunctions of two boundary value problems for three-dimensional equations of elliptic types with singular coefficients with lower terms are found.
Karimov K. T.
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Positive solutions for singular critical elliptic problems
Applied Mathematics Letters, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dongsheng Kang, Shuangjie Peng
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A shallow Ritz method for elliptic problems with singular sources
Journal of Computational Physics, 2022 In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) the delta function singularity is naturally removed, (ii) level set function is introduced as a feature input, (iii) it is completely shallow,
Te-Sheng Lin
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Boundary Value Problems for Singular Elliptic Equations
Rocky Mountain Journal of Mathematics, 2011 Let \(\Omega\subset\mathbb R^N\) be a bounded domain with smooth boundary, \(a:\Omega\rightarrow [1,+\infty)\) a bounded function, \(h:[0,+\infty)\rightarrow\mathbb R\) continuous, and \(g:(0,+\infty)\rightarrow\mathbb R\) a continuous function such that \(\lim_{s\rightarrow 0^+}g(s)=+\infty\). Fix \(p>1\).
Klaus Schmitt
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Potentials for a three-dimensional elliptic equation with one singular coefficient and their application [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 A potential theory for a three-dimensional elliptic equation with one singular coefficient is considered. Double- and simple-layer potentials with unknown density are introduced, which are expressed in terms of the fundamental solution of the mentioned ...
Tuhtasin G. Ergashev
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Potentials for the singular elliptic equations and their application
Results in Applied Mathematics, 2020 Potential theory has played a paramount role in both analysis and computation for boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one ...
T.G. Ergashev
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Uniqueness results for elliptic problems with singular data
Boundary Value Problems, 2006 We obtain some uniqueness results for the Dirichlet problem for second-order elliptic equations in an unbounded open set without the cone property, and with data depending on appropriate weight functions.
Caso Loredana
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The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term
Advanced Nonlinear Studies, 2021 In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice ...
Esposito Francesco, Sciunzi Berardino
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Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients [PDF]
, 2013 This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and
Mikhailov, SE +2 more
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