Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions
Sign Up to like & getrecommendations! Published in 2018 at "Numerische Mathematik"
DOI: 10.1007/s00211-017-0899-1
Abstract: We analyze the approximation of the solutions of second-order elliptic problems, which have point singularities and belong to a countably normed space of analytic functions, with a first-order, h-version finite element (FE) method based on… read more here.
Keywords: order; second order; tensor; tensor structured ... See more keywords
A Bivariate Spline Method for Second Order Elliptic Equations in Non-divergence Form
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-017-0562-0
Abstract: A bivariate spline method is developed to numerically solve second order elliptic partial differential equations in non-divergence form. The existence, uniqueness, stability as well as approximation properties of the discretized solution will be established by… read more here.
Keywords: bivariate spline; spline method; second order; order elliptic ... See more keywords
Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2017.05.011
Abstract: Abstract We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the bi-harmonic… read more here.
Keywords: order elliptic; stability results; higher order; elliptic operators ... See more keywords
The p-ellipticity condition for second order elliptic systems and applications to the Lamé and homogenization problems
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DOI: 10.1016/j.jde.2021.08.036
Abstract: The notion of $p$-ellipticity has recently played a significant role in improving our understanding of issues of solvability of boundary value problems for scalar complex valued elliptic PDEs. In particular, the presence of $p$-ellipticity ensures… read more here.
Keywords: ellipticity; second order; order elliptic; homogenization ... See more keywords
On the boundary estimates for second-order elliptic equations
Sign Up to like & getrecommendations! Published in 2018 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2017.1420066
Abstract: Abstract Consider uniformly elliptic equations in general form in a domain . We discuss the minimal assumptions on the boundary of which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided . The… read more here.
Keywords: estimates second; second order; equations boundary; elliptic equations ... See more keywords
Representations of the solutions of the first-order elliptic and hyperbolic systems via harmonic and wave functions respectively
Sign Up to like & getrecommendations! Published in 2019 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2019.1669570
Abstract: ABSTRACT In this paper representations of the solutions of all first-order elliptic and hyperbolic systems in three-dimensional and four-dimensional spaces are obtained through the derivatives of harmonic and wave functions, respectively. read more here.
Keywords: representations solutions; hyperbolic systems; first order; order elliptic ... See more keywords
On positive solution to a second order elliptic equation with a singular nonlinearity
Sign Up to like & getrecommendations! Published in 2019 at "Communications on Pure and Applied Analysis"
DOI: 10.3934/cpaa.2010.9.1335
Abstract: We consider a second order elliptic equation with measurable bounded coefficients $ (a_{ij}(x)u_{x_i})_{x_j}+p(x)|x|^su^{-\sigma}=0, x\in\Omega \setminus \{ O\}, $ where $\sigma >0$, $s$ is any real number, and $\Omega\subset R^n$, $n\ge 3$ is a bounded domain,… read more here.
Keywords: elliptic equation; positive solution; order elliptic; second order ... See more keywords