Results 131 to 140 of about 444 (158)

The Dirichlet Problem for Elliptic Equations with VMO Coefficients in Generalized Morrey Spaces

, 2013
We consider the Dirichlet problem in a bounded smooth domain \( \Omega \subset \mathbb{R}^{n} \) for linear uniformly elliptic equation \( \mathfrak{L}u(x)=f(x) \) with VMO principal coefficients. Its unique strong solvability is proved in [5] and [6]. Our aim is to show that for every f belonging to the generalized Morrey space \( L^{p,\omega}(\Omega),
SOFTOVA Lyoubomira, SOFTOVA PALAGACHEVA, Lyoubomira, Lubomira G. Softova   +2 more
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Second-order elliptic equations with variably partially VMO coefficients

Journal of Functional Analysis, 2009
The solvability in Wp2(Rd) spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball.
N V Krylov
exaly   +2 more sources

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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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Equations with VMO coefficients

, 2008
N. Krylov
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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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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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On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains

St. Petersburg Mathematical Journal, 2012
The paper is devoted to fully nonlinear elliptic and parabolic equations with vanishing mean oscillation coefficients in bounded domains or cylinders. The systems under consideration particularly cover parabolic Bellman's equations. The solvability in the Sobolev spaces of the terminal-boundary value problem is proved. The solvability in \(W^{1,2}_p\),
Dong, Hongjie, Krylov, N. V., Li, Xu
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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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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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Quasilinear parabolic equations with VMO coefficients

2000
This paper deals with the Cauchy-Dirichlet problem and with the regular oblique derivative problem for quasilinear parabolic operators with discontinuous coefficients. To be more precise, the coefficients belong to the VMO class and the right hand side has a quadratic growth with respect to the gradient.
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