Infinite dimension of solutions of the Dirichlet problem
Open Mathematics, 2015 It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.
Ryazanov Vladimir
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Solving a Dirichlet problem on unbounded domains via a conformal transformation [PDF]
Mathematische Annalen, 2022 In this paper, we solve the p-Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure satisfying a Poincaré inequality. This is accomplished by studying a class of
Ryan Gibara, R. Korte, N. Shanmugalingam
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Existence of radial solutions for a p ( x ) $p(x)$ -Laplacian Dirichlet problem
Advances in Differential Equations, 2021 In this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized p ( x ) $p(x)$ -Laplacian problem − Δ p ( x ) u + R ( x ) u p ( x ) − 2 u = a ( x ) | u | q ( x ) − 2 u − b ( x ) | u | r ( x ) −
M. Ragusa, A. Razani, F. Safari
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The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation [PDF]
Comptes rendus. Mathematique, 2020 The Cauchy-Dirichlet problem for the Moore-Gibson-Thompson equation is analyzed. With the focus on non-homogeneous boundary data, two approaches are offered: one is based on the theory of hyperbolic systems, while the other one uses the theory of ...
F. Bucci, M. Eller
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On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians [PDF]
Journal of Differential Equations, 2020 In this paper, we show the existence of a sequence of eigenvalues for a Dirichlet problem involving two mixed fractional operators with different orders. We provide lower and upper bounds for the sum of the eigenvalues.
Huyuan Chen, M. Bhakta, H. Hajaiej
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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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Parabolic and elliptic equations with singular or degenerate coefficients: The Dirichlet problem [PDF]
, 2020 We consider the Dirichlet problem for a class of elliptic and parabolic equations in the upper-half space $\mathbb{R}^d_+$, where the coefficients are the product of $x_d^\alpha, \alpha \in (-\infty, 1),$ and a bounded uniformly elliptic matrix of ...
Hongjie Dong, T. Phan
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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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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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