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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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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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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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The Dirichlet problem on quadratic surfaces [PDF]
Mathematics of Computation, 2003 We give a fast, exact algorithm for solving Dirichlet problems with polynomial boundary functions on quadratic surfaces in R
Sheldon Axler, Pamela Gorkin, Karl Voss
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The hyperbolic dirichlet problem
Mathematical and Computer Modelling, 2000 The authors show that there are uncountably many rotations, that assure the existence and uniqueness of the solution to the hyperbolic Dirichlet problem for a transitive curve being an ellipse. Moreover, a numerical algorithm for the computation of the solution is presented.
Pavani, R., Talamo, R.
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Journal für die reine und angewandte Mathematik (Crelles Journal), 1984 Let S(U) denote the cone of all P-bounded real continuous functions on a P-harmonic space \((X,^*H)\) which are superharmonic on the open subset \(U\subseteq X\). The authors have previously shown [Invent. Math. 29, 83- 110 (1975; Zbl 0308.31011)] that \(S(U)\) is implying that the weak Dirichlet problem is solvable: For any compact subset \(K\subseteq
Hansen, W., Bliedner, J.
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Časopis pro pěstování matematiky, 1958 Let S + be a connected region, bounded by simple smooth non- intersecting contours Lo, L1 …, LP the first of which contains all the others. By L will be understood the union of these contours; as usual, the positive direction on L will be taken such that S + remains on the left. The contour Lo may be absent in which case S+ is infinite.
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Constructive Aspects of the Dirichlet Problem
J. Univers. Comput. Sci., 1997 JUCS - Journal of Universal Computer Science Volume Nr.
Bridges,Douglas, Yuchuan,Wang
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