Dirichlet Duality and the Nonlinear Dirichlet Problem [PDF]
Communications on Pure and Applied Mathematics, 2007 We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form f(Hess, u)=0 on a smoothly bounded domain D in R^n. In our approach the equation is replaced by a subset F of the space of symmetric nxn-matrices, with bdy(F ...
Harvey, F. Reese, Lawson, Jr, H. Blaine
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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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A Dirichlet problem in the strip
Electronic Journal of Differential Equations, 1996 In this paper we investigate a Dirichlet problem in a strip and, using the sliding method, we prove monotonicity for positive and bounded solutions. We obtain uniqueness of the solution and show that this solution is a function of only one variable. From
Eugenio Montefusco
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The Dirichlet problem for nonlocal operators [PDF]
Mathematische Zeitschrift, 2014 In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a given bounded set.
Felsinger, Matthieu +2 more
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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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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 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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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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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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