Results 1 to 10 of about 26,670 (302)
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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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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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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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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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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The problem of Dirichlet for an ellipsoid [PDF]
Terrestrial Magnetism and Atmospheric Electricity, 1935 (1) Introduction—In a group of important problems in potential theory it is required to determine a harmonic function which takes on preassigned continuous values on the boundaries of some region R. Under the proper limitations on the geometrical characteristics of the region R, it is known that the solution of the problem of Dirichlet exists and is ...
Sokolnikoff, I. S., Sokolnikoff, E. S.
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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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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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Petviashvilli’s Method for the Dirichlet Problem [PDF]
Journal of Scientific Computing, 2015 We examine the Petviashvilli method for solving the equation $ ϕ- Δϕ= |ϕ|^{p-1} ϕ$ on a bounded domain $Ω\subset \mathbb{R}^d$ with Dirichlet boundary conditions. We prove a local convergence result, using spectral analysis, akin to the result for the problem on $\mathbb{R}$ by Pelinovsky & Stepanyants, 2004.
Derek Olson +3 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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