Schrödinger operators with δ and δ′-potentials supported on hypersurfaces [PDF]
, 2013 Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions.
Lotoreichik, Vladimir +2 more
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Singular elliptic problems in general domains [PDF]
, 2023 In this paper, we prove the existence of solutions to nonlinear elliptic equations, which present first-order terms with natural growth with respect to the gradient and lower order terms singular in the variable that represents the solution. The problems
de Bonis, I
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Symmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball [PDF]
, 2004 In [40], it was shown that the following singularly perturbed Dirichlet problem \ep^2 \Delta u - u+ |u|^{p-1} u=0, \ \mbox{in} \ \Om,\] \[ u=0 \ \mbox{on} \ \partial \Om has a nodal solution u_\ep which has the least energy among all nodal solutions.
Winter, M +5 more
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On elliptic problems with Choquard term and singular nonlinearity
Asymptotic Analysis, 2022 Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded a.e. in the domain Ω and is Hölder continuous.
Choudhuri, Debajyoti +2 more
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Higher order energy expansions for some singularly perturbed Neumann problems [PDF]
, 2003 We consider the following singularly perturbed semilinear elliptic problem: \epsilon^{2} \Delta u - u + u^p=0 \ \ \mbox{in} \ \Omega, \quad u>0 \ \ \mbox{in} \ \ \Omega \quad \mbox{and} \ \frac{\partial u}{\partial \nu} =0 \ \mbox{on} \ \partial \
Winter, M +5 more
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An elliptic problem of the Prandtl–Batchelor type with a singularity
Boundary Value Problems, 2023 AbstractWe establish the existence of at least two solutions of the Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable, and hence the usual variational techniques do not work.
Choudhuri, Debajyoti, Repovš, Dušan
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Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains [PDF]
, 2002 Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of ...
M. Mitrea +3 more
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Singular Integral Operators and Elliptic Boundary-Value Problems. I
Современная математика: Фундаментальные направления, 2017 The book consists of three Parts I-III and Part I is presented here. In this book, we develop a new approach mainly based on the authors papers. Many results are published here for the first time. Chapter 1 is introductory.
Alexandre P Soldatov
doaj +1 more source
Singular Higher Order Divergence-Conforming Bases of Additive Kind and Moments Method Applications to 3D Sharp-Wedge Structures [PDF]
, 2008 We present new subsectional, singular divergence conforming vector bases that incorporate the edge conditions for conducting wedges. The bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other ...
GRAGLIA, Roberto +2 more
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Solution regularity and co-normal derivatives for elliptic systems with non-smooth coefficients on Lipschitz domains [PDF]
, 2013 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 ElsevierElliptic PDE systems of the second order with coefficients from L∞ or Holder-Lipschitz spaces are considered in ...
Mikhailov, SE
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