On a generalization of the Neumann problem for the Laplace equation
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201800219
Abstract: We investigate solvability of a fractional analogue of the Neumann problem for the Laplace equation. As a boundary operator we consider operators of fractional differentiation in the Hadamard sense. The problem is solved by reduction… read more here.
Keywords: neumann problem; laplace equation; problem; equation ... See more keywords
A high‐order harmonic polynomial method for solving the Laplace equation with complex boundaries and its application to free‐surface flows. Part I: Two‐dimensional cases
Sign Up to like & getrecommendations! Published in 2020 at "International Journal for Numerical Methods in Engineering"
DOI: 10.1002/nme.6390
Abstract: A high‐order harmonic polynomial method (HPM) is developed for solving the Laplace equation with complex boundaries. The “irregular cell” is proposed for the accurate discretization of the Laplace equation, where it is difficult to construct… read more here.
Keywords: method; complex boundaries; laplace equation; free surface ... See more keywords
The Christoffel problem by the fundamental solution of the Laplace equation
Sign Up to like & getrecommendations! Published in 2019 at "Science China Mathematics"
DOI: 10.1007/s11425-019-1674-1
Abstract: The Christoffel problem is equivalent to the existence of convex solutions to the Laplace equation on the unit sphere $${{\mathbb S}^n}$$ S n . Necessary and sufficient conditions have been found by Firey (1967) and… read more here.
Keywords: laplace equation; christoffel problem; problem;
The implementation of the Laplace equation in a slope stability analysis: the streamline method
Sign Up to like & getrecommendations! Published in 2020 at "Acta Geotechnica"
DOI: 10.1007/s11440-020-01047-y
Abstract: The Laplace equation satisfies the principle of the minimum potential energy, which means that groundwater flows through soil in an optimized path of minimal energy under a given condition. The essential idea of the proposed… read more here.
Keywords: laplace equation; proposed method; slope stability; method ... See more keywords
High-accuracy quadrature methods for solving nonlinear boundary integral equations of axisymmetric Laplace’s equation
Sign Up to like & getrecommendations! Published in 2018 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-018-0714-3
Abstract: In this article, we study the numerical solutions of axisymmetric Laplace’s equation with nonlinear boundary conditions. The problem could be converted into nonlinear boundary integral equations by the ring potential theory. The mechanical quadrature method… read more here.
Keywords: laplace equation; axisymmetric laplace; accuracy; boundary integral ... See more keywords
Boundary behavior of solutions to the parabolic p-Laplace equation II
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2020.108515
Abstract: Abstract This paper is the second installment in a series of papers concerning the boundary behavior of solutions to the p-parabolic equations. In this paper we are interested in the short time behavior of the… read more here.
Keywords: laplace equation; parabolic laplace; boundary behavior; behavior solutions ... See more keywords
A novel efficient numerical solution of Laplace equation with mixed boundary conditions
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2021.1967939
Abstract: This paper describes a new type of method to solve Laplace equation subject to mixed boundary conditions in two-dimensional domains for electrostatics. The electric potential ϕ is represented by harmonic Steklov eigenfunctions, obtained from a… read more here.
Keywords: boundary conditions; efficient numerical; mixed boundary; laplace equation ... See more keywords
Spheroidal harmonic expansions for the solution of Laplace's equation for a point source near a sphere.
Sign Up to like & getrecommendations! Published in 2017 at "Physical Review E"
DOI: 10.1103/physreve.95.033307
Abstract: We propose a powerful approach to solve Laplace's equation for point sources near a spherical object. The central new idea is to use prolate spheroidal solid harmonics, which are separable solutions of Laplace's equation in… read more here.
Keywords: laplace equation; equation; equation point; solution laplace ... See more keywords
Radially Symmetric Solutions of the p-Laplace Equation with Gradient Terms
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Applied and Industrial Mathematics"
DOI: 10.1134/s1990478918040178
Abstract: We consider the Dirichlet problem for the p-Laplace equation with nonlinear gradient terms. In particular, these gradient terms cannot satisfy the Bernstein—Nagumo conditions. We obtain some sufficient conditions that guarantee the existence of a global… read more here.
Keywords: laplace equation; radially symmetric; gradient terms; symmetric solutions ... See more keywords
On Conformable Laplace’s Equation
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Problems in Engineering"
DOI: 10.1155/2021/5514535
Abstract: The most important properties of the conformable derivative and integral have been recently introduced. In this paper, we propose and prove some new results on conformable Laplace’s equation. We discuss the solution of this mathematical… read more here.
Keywords: laplace equation; conformable laplace;
Numerical Method for a Cauchy Problem for Multi-Dimensional Laplace Equation with Bilateral Exponential Kernel
Sign Up to like & getrecommendations! Published in 2023 at "Mathematics"
DOI: 10.3390/math11081855
Abstract: This study examined a Cauchy problem for a multi-dimensional Laplace equation with mixed boundary. This problem is severely ill-posed in the sense of Hadamard. To solve this problem, a mollification approach is suggested based on… read more here.
Keywords: problem; problem multi; cauchy problem; laplace equation ... See more keywords