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On the Exterior Dirichlet Problem for Monge–Ampère Equations
Journal of Mathematical Analysis and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiguang Bao, Hongjie Ju
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The Exterior Dirichlet Problem for Hessian Quotient Equations
Journal of Mathematical Analysis and Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haigang Li, Limei Dai
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2020
The exterior Dirichlet problem consists in finding u such that $$\displaystyle \begin {array}{rl} &Au(x)=0,\quad x\in S^-,\\ &u(x)=\mathscr {D}(x),\quad x\in {\partial S},\\ &u\in \mathscr {A}^*, \end {array} $$ where the vector function \(\mathscr {D}\in C^{(1,\alpha )}({\partial S})\), α ∈ (0, 1), is prescribed.
Christian Constanda, Dale Doty
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The exterior Dirichlet problem consists in finding u such that $$\displaystyle \begin {array}{rl} &Au(x)=0,\quad x\in S^-,\\ &u(x)=\mathscr {D}(x),\quad x\in {\partial S},\\ &u\in \mathscr {A}^*, \end {array} $$ where the vector function \(\mathscr {D}\in C^{(1,\alpha )}({\partial S})\), α ∈ (0, 1), is prescribed.
Christian Constanda, Dale Doty
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The exterior dirichlet problem for the Laplace equation
Mathematical Methods in the Applied Sciences, 1985AbstractUsing a standard application of Green's theorem, the exterior Dirichlet problem for the Laplace equation in three dimensions is reduced to a pair of integral equations. One integral equation is of the second kind and the other is of the first kind.
J. F. Ahner, G. C. Hsiao
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Random Walk on Spheres Process for Exterior Dirichlet Problem
Monte Carlo Methods and Applications, 1995A random walk on spheres process is constructed to solve the problem \(\Delta u(x)= 0\), \(x\in \mathbb{R}^3\backslash \overline G\), \(u|_\Gamma= \varphi\), \(u(x)\to 0\) for \(|x|\to \infty\).
Karl K. Sabelfeld, Irina A. Shalimova
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Dirichlet–Neumann Problem for the Biharmonic Equation in Exterior Domains
Differential Equations, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Estimates of the Solution of the Dirichlet Problem for the Laplace Operator in Exterior Domains
Journal of Soviet Mathematics, 1988Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 146, 92-101 (Russian) (1985; Zbl 0605.35021).
V A Solonnikov
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On the Exterior Dirichlet Problem for the Monge–Ampère Equation in Dimension Two
Nonlinear Analysis: Theory, Methods & Applications, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiguang Bao, Haigang Li
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Singular Perturbation of an Exterior Dirichlet Problem
SIAM Journal on Mathematical Analysis, 1978This paper discusses a class of singular perturbation problems such as those of slow viscous flow past a cylinder. A semilinear second-order elliptic equation with a small parameter is used as a model to illustrate the correlation between a regular perturbation procedure and the method of matched asymptotic expansions.
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On the Continuous Dependence of the Exterior Dirichlet Problem on the Boundary
Mathematical Methods in the Applied Sciences, 1997Summary: We consider a sequence of exterior domains \(D_j\), \(j\in\mathbb{N}_0\), and assume that the boundaries \(\partial D_j\) converge to \(\partial D_0\) with respect to the Hausdorff distance. We investigate solutions to the exterior Dirichlet problem for the Laplace equation and for the Helmholtz equation in these domains.
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