Results 11 to 20 of about 12,245,009 (305)
Applied Mathematics Letters, 2020 In this paper, we focus on the convergence analysis of the unique solution for a Dirichlet problem of the general k -Hessian equation in a ball. By introducing some suitable growth conditions and developing a new iterative technique, the unique solution ...
Xinguang Zhang +4 more
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The Dirichlet problem for the k-Hessian equation on a complex manifold [PDF]
American Journal of Mathematics, 2019 :We solve the Dirichlet problem for $k$-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a particular gradient
Tristan C. Collins, Sebastien Picard
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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 Regularity of Minima for the Dirichlet Problem on BD
Archive for Rational Mechanics and Analysis, 2020 We establish that the Dirichlet problem for linear growth functionals on $${\text {BD}}$$ BD , the functions of bounded deformation, gives rise to the same unconditional Sobolev and partial $${\text {C}}^{1,\alpha }$$ C 1 , α -regularity theory as ...
Franz Gmeineder
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The Dirichlet problem for the logarithmic Laplacian [PDF]
Communications in Partial Differential Equations, 2017 In this article, we study the logarithmic Laplacian operator which is a singular integral operator with symbol We show that this operator has the integral representation with and where Γ is the Gamma function, is the Digamma function and is the Euler ...
Huyuan Chen, T. Weth
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A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian [PDF]
Computers and Mathematics with Applications, 2016 In Acosta etal. (2017), a complete n-dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we provide a comprehensive and simple 2D MATLAB finite element code for such a problem.
Gabriel Acosta +2 more
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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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The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary [PDF]
, 2012 We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of ( − Δ ) s u = g in Ω, u ≡ 0 in R n \ Ω , for some s ∈ ( 0 , 1 ) and g ∈ L ∞ ( Ω ) , then u is C s ( R n ...
Xavier Ros-Oton, J. Serra
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Some recent results on the Dirichlet problem for $(p, q)$-Laplace equations [PDF]
, 2017 A short account of recent existence and multiplicity theorems on the Dirichlet problem for an elliptic equation with $(p, q)$-Laplacian in a bounded domain is performed.
S. Marano, S. Mosconi
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A viscosity approach to the Dirichlet problem for degenerate complex Hessian-type equations [PDF]
Analysis & PDE, 2017 A viscosity approach is introduced for the Dirichlet problem associated to complex Hessian type equations on domains in $\C^n$. The arguments are modelled on the theory of viscosity solutions for real Hessian type equations developed by Trudinger.
S. Dinew, H. Do, T. To
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