Irregular Elliptic Boundary-Value Problems and Hörmander Spaces
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DOI: 10.1007/s11253-018-1504-1
Abstract: We study irregular elliptic problems with boundary operators of higher orders and prove that these problems are Fredholm on appropriate pairs of the inner-product Hörmander spaces that form a two-sided refined Sobolev scale. We prove… read more here.
Keywords: problems rmander; irregular elliptic; boundary value; elliptic boundary ... See more keywords
The optimal convergence of finite element methods for the three-dimensional second-order elliptic boundary value problem with singularity
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DOI: 10.1016/j.jmaa.2020.124369
Abstract: Abstract Let x 0 ∈ Ω . Assume that G x 0 ( x ) satisfies the elliptic boundary value problem L G x 0 ( x ) ≡ ∂ ∂ x j ( a… read more here.
Keywords: value problem; elliptic boundary; boundary value; finite element ... See more keywords
Elliptic boundary value problems with Gaussian white noise loads
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DOI: 10.1016/j.spa.2017.11.007
Abstract: Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. Especially, Neumann and Robin BVPs are considered. The main obstacle for applying the… read more here.
Keywords: noise loads; boundary value; noise; gaussian white ... See more keywords
PERTURBATIONS FROM INDEFINITE SYMMETRIC ELLIPTIC BOUNDARY VALUE PROBLEMS
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DOI: 10.1017/s0017089516000446
Abstract: Abstract In this paper, we study the multiplicity of solutions for the following problem: $$\begin{equation*} \begin{cases} -\Delta u-\Delta(|u|^{\alpha})|u|^{\alpha-2}u=g(x,u)+\theta h(x,u), \ \ x\in \Omega,\\ u=0, \ \ x\in \partial\Omega, \end{cases} \end{equation*}$$ where α ≥ 2, Ω… read more here.
Keywords: indefinite symmetric; value problems; symmetric elliptic; boundary value ... See more keywords