Results 121 to 130 of about 300 (152)

Regularity of Solutions to Elliptic Equations with VMO Coefficients

Acta Mathematica Sinica, English Series, 2004
The paper deals with the Lebesgue and Morrey regularity of solutions to the Dirichlet problems for linear second-order, uniformly elliptic equations both in divergence form \[ Mu\equiv -(a_{ij}u_{x_i}+b_ju)_{x_j} +c_ju_{x_j}+du=e+(f_j)_{x_j}, \] and in non-divergence form \[ Lu\equiv a_{ij}u_{x_ix_j}+b_iu_{x_i} +cu=f. \] The principal coefficients \(a_{
exaly   +3 more sources

Riesz transforms and elliptic PDEs with VMO coefficients

Journal d'Analyse Mathématique, 1998
Let \(A:\Omega\to \mathbb{R}^{n^2}\) be a measurable matrix function in an open set \(\Omega\subset \mathbb{R}^n\). The authors are concerned with the \(A\)-harmonic operator \(\text{\textsterling} u:= \text{div}(A\nabla u)\) acting on the Sobolev space \(W^{1,p}_0(\Omega)\). It is assumed that \textsterling{} is uniformly elliptic and that the entries
T. IWANIEC, SBORDONE, CARLO
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Quaternionic Beltrami Equations with VMO Coefficients

The Journal of Geometric Analysis, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Parabolic equations with VMO coefficients in generalized Morrey spaces

Acta Mathematica Sinica, English Series, 2010
The authors consider solvability of the oblique derivative problem for linear uniformly parabolic operators with VMO coefficients in some kind of Morrey spaces.
Jiang Zhou
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Anisotropic elliptic equations with VMO coefficients

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Optimal regular differential operators with VMO coefficients

AIP Conference Proceedings, 2012
This paper presents the study of maximal regularity properties for elliptic differential-operator equations with VMO coefficients. We prove that the corresponding elliptic operator is separable, positive and is a generator of an analytic semigroup in vector-valued Lp spaces.
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Weighted solution of the Dirac Beltrami equation with coefficient in VMO

Complex Variables and Elliptic Equations, 2016
We study the generalized Beltrami equation , where is the left Dirac operator in acting on functions in and with values in the complex Clifford algebra , is its conjugate, and is a -valued function with compact support, with vanishing mean oscillation, satisfying , where are the coordinates of in . Let be a weight function in . We prove that if belongs
Victor Cruz, Emilio Marmolejo-Olea, Salvador Pérez-Esteva   +2 more
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Oblique derivative problem for parabolic operators with VMO coefficients

manuscripta mathematica, 2000
The paper deals with the regular oblique derivative problem \[ \left\{ \begin{aligned} u_t-\sum_{i,j=1}^n a_{ij}(x,t) D_{ij}u=f(x,t)\quad &\text{ a.e. in} Q_T,\\ u(x,0)=\varphi(x) &\quad \text{on} \Omega,\\ \sum_{i=1}^n \ell_i(x,t)D_i u=\psi(x,t)\quad &\text{on} S_T,\end{aligned}\right.\tag \(*\) \] where \(Q_T\) is a cylinder in \({\mathbb R}^n\times {
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Uniqueness results for elliptic equations with VMO-coefficients

2004
In this paper we prove some uniqueness results for the Dirichlet problem for linear elliptic equations with locally VMO coefficients in unbounded domains.
CASO, Loredana, CAVALIERE, Paola, TRANSIRICO, Maria   +2 more
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Very Weak Solutions of p-Laplacian Type Equations with VMO Coefficients

Journal of Partial Differential Equations, 2001
Summary: We obtain a new a priori estimate for the very weak solutions of \(p\)-Laplacian type equations with VMO coefficients when \(p\) is close to 2, and prove that the very weak solutions of such equations are the usual weak solutions. Our approach is based on the Hodge decomposition and the \(L^p\)-estimate for the corresponding linear equations ...
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