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The Approximate Solution of 2D Dirichlet Problem in Doubly Connected Domains [PDF]
Advances in Mathematical Physics, 2018 We propose a new method for constructing an approximate solution of the two-dimensional Laplace equation in an arbitrary doubly connected domain with smooth boundaries for Dirichlet boundary conditions.
Atallah El-shenawy, Elena A. Shirokova
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On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball
Axioms, 2023 The paper gives an explicit representation of the Green’s function of the Dirichlet boundary value problem for the polyharmonic equation in the unit ball. The solution of the homogeneous Dirichlet problem is found.
Valery Karachik
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Higher order Nevanlinna functions and the inverse three spectra problem [PDF]
Opuscula Mathematica, 2016 The three spectra problem of recovering the Sturm-Liouville equation by the spectrum of the Dirichlet-Dirichlet boundary value problem on \([0,a]\), the Dirichlet-Dirichlet problem on \([0,a/2]\) and the Neumann-Dirichlet problem on \([a/2,a]\) is ...
Olga Boyko +2 more
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Dirichlet Problem with L1(S) Boundary Values
Axioms, 2022 Let D be a connected bounded domain in R2, S be its boundary, which is closed and C2-smooth. Consider the Dirichlet problem Δu=0inD,u|S=h, where h∈L1(S).
Alexander G. Ramm
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Mathematics, 2022 In this research, we investigate an optimal control problem governed by elliptic PDEs with Dirichlet boundary conditions on complex connected domains, which can be utilized to model the cooling process of concrete dam pouring.
Mengya Su, Liuqing Xie, Zhiyue Zhang
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Dirichlet duality and the nonlinear Dirichlet problem [PDF]
Communications on Pure and Applied Mathematics, 2008 AbstractWe study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F(Hess u) = 0 on a smoothly bounded domain Ω ⋐ ℝn. In our approach the equation is replaced by a subset F ⊂ Sym2(ℝn) of the symmetric n × n matrices with ∂F ⊆ {F = 0}.
Harvey, F. Reese, Lawson, H. Blaine jun.
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The Dirichlet Casimir problem [PDF]
Nuclear Physics B, 2004 Casimir forces are conventionally computed by analyzing the effects of boundary conditions on a fluctuating quantum field. Although this analysis provides a clean and calculationally tractable idealization, it does not always accurately capture the characteristics of real materials, which cannot constrain the modes of the fluctuating field at all ...
Graham, N. +5 more
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Recovering the shape of an equilateral quantum tree with the Dirichlet conditions at the pendant vertices [PDF]
Opuscula MathematicaWe consider two spectral problems on an equilateral rooted tree with the standard (continuity and Kirchhoff's type) conditions at the interior vertices (except of the root if it is interior) and Dirichlet conditions at the pendant vertices (except of the
Anastasia Dudko +2 more
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On Ambarzumian type theorems for tree domains [PDF]
Opuscula Mathematica, 2022 It is known that the spectrum of the spectral Sturm-Liouville problem on an equilateral tree with (generalized) Neumann's conditions at all vertices uniquely determines the potentials on the edges in the unperturbed case, i.e. case of the zero potentials
Vyacheslav Pivovarchik
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Dirichlet and Neumann Boundary Value Problems for the Polyharmonic Equation in the Unit Ball
Mathematics, 2021 In the previous author’s works, a representation of the solution of the Dirichlet boundary value problem for the biharmonic equation in terms of Green’s function is found, and then it is shown that this representation for a ball can be written in the ...
Valery Karachik
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