The Experts below are selected from a list of 37608 Experts worldwide ranked by ideXlab platform
Hongjie Dong - One of the best experts on this subject based on the ideXlab platform.
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lp estimates for time fractional parabolic equations in Divergence Form with measurable coefficients
Journal of Functional Analysis, 2020Co-Authors: Hongjie Dong, Doyoon KimAbstract:Abstract In this paper, we establish L p -estimates and solvability for time fractional Divergence Form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean oscillations with respect to the other variables. The corresponding results for equations on a half space are also derived.
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Gradient Estimates for Divergence Form Elliptic Systems Arising from Composite Material
SIAM Journal on Mathematical Analysis, 2019Co-Authors: Hongjie DongAbstract:In this paper, we show that $W^{1,p}$ $(1\leq p < \infty)$ weak solutions to Divergence Form elliptic systems are Lipschitz and piecewise $C^{1}$ provided that the leading coefficients and data are...
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solvability of parabolic equations in Divergence Form with partially bmo coefficients
Journal of Functional Analysis, 2010Co-Authors: Hongjie DongAbstract:Abstract We prove the H p 1 solvability of second order parabolic equations in Divergence Form with leading coefficients a i j measurable in ( t , x 1 ) and having small BMO (bounded mean oscillation) semi-norms in the other variables. Additionally we assume a 11 is measurable in x 1 and has small BMO semi-norms in the other variables. The corresponding results for the Cauchy problem are also established. Parabolic equations in Sobolev spaces H q , p 1 with mixed norms are also considered under the same conditions of the coefficients.
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elliptic equations in Divergence Form with partially bmo coefficients
arXiv: Analysis of PDEs, 2008Co-Authors: Hongjie Dong, Doyoon KimAbstract:The solvability in Sobolev spaces is proved for Divergence Form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients $a^{ij}$ are assumed to be measurable in one direction and have small BMO semi-norms in the other directions. For equations in a bounded domain, additionally we assume that $a^{ij}$ have small BMO semi-norms in a neighborhood of the boundary of the domain. We give a unified approach of both the Dirichlet boundary problem and the conormal derivative problem. We also investigate elliptic equations in Sobolev spaces with mixed norms under the same assumptions on the coefficients.
Nicolai V Krylov - One of the best experts on this subject based on the ideXlab platform.
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On Divergence Form Second-order PDEs with Growing Coefficients
2011Co-Authors: Nicolai V KrylovAbstract:We consider second-order Divergence Form uniFormly parabolic and elliptic PDEs with bounded and VM O x leading coefficients and possibly lin- early growing lower-order coefficients. We look for solutions which are sum- mable to the pth power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variables.
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On Divergence Form SPDEs with VMO coefficients in a half space
Stochastic Processes and their Applications, 2009Co-Authors: Nicolai V KrylovAbstract:We extend several known results on solvability in the Sobolev spaces , p[set membership, variant][2,[infinity]), of SPDEs in Divergence Form in to equations having coefficients which are discontinuous in the space variable.
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On Divergence Form SPDEs with VMO coefficients
arXiv: Probability, 2008Co-Authors: Nicolai V KrylovAbstract:We present several results on solvability in Sobolev spaces $W^{1}_{p}$ of SPDEs in Divergence Form in the whole space.
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On Divergence Form SPDEs with VMO coefficients in a half space
arXiv: Probability, 2008Co-Authors: Nicolai V KrylovAbstract:We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in Divergence Form in $\bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.
Jean-marc Bouclet - One of the best experts on this subject based on the ideXlab platform.
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Low frequency estimates for long range perturbations in Divergence Form
Canadian Journal of Mathematics, 2011Co-Authors: Jean-marc BoucletAbstract:We prove a uniForm control as z → 0 for the resolvent (P−z)−1 of long range perturbations P of the Euclidean Laplacian in Divergence Form, by combining positive commutator estimates and properties of Riesz transForms. These estimates hold in dimension d ≥ 3 when P is defined on R, and in dimension d ≥ 2 when P is defined outside a compact obstacle with Dirichlet boundary conditions.
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Low frequency estimates for long range perturbations in Divergence Form
arXiv: Analysis of PDEs, 2008Co-Authors: Jean-marc BoucletAbstract:We prove low frequency estimates for the boundary values of the resolvent of long range perturbations of the flat Laplacian in Divergence Form.
Treven Wall - One of the best experts on this subject based on the ideXlab platform.
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THE L p DIRICHLET PROBLEM FOR SECOND-ORDER, NON-Divergence Form OPERATORS: SOLVABILITY AND PERTURBATION RESULTS
Journal of Functional Analysis, 2011Co-Authors: Martin Dindoš, Treven WallAbstract:We establish Dahlberg's perturbation theorem for non-Divergence Form operators L = Ar 2 . If L0 and L1 are two operators on a Lipschitz domain such that the L p Dirichlet problem for the operator L0 is solvable for some p 2 (1,1 ) and the coefficients of the two operators are sufficiently close in the sense of Carleson measure, then the L p Dirichlet problem for the operator L1 is solvable for the same p. This is an improvement of the A1 version of this result proved by Rios in (10). As a consequence we also improve a result from (4) for the L p solvability of non-Divergence Form operators (Theorem 3.2) by substantially weakening the condition required on the coefficients of the operator. The improved condition is exactly the same one as is required for Divergence Form operators L = div Ar .
Kyeong Hun Kim - One of the best experts on this subject based on the ideXlab platform.
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An Lp-theory of Stochastic PDEs of Divergence Form on Lipschitz Domains
Journal of Theoretical Probability, 2008Co-Authors: Kyeong Hun KimAbstract:Stochastic partial differential equations of Divergence Form are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces. It is allowed that the coefficients of the equations substantially oscillate or blow up near the boundary.
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on lp theory of stochastic partial differential equations of Divergence Form in c1 domains
Probability Theory and Related Fields, 2004Co-Authors: Kyeong Hun KimAbstract:Stochastic partial differential equations of Divergence Form are considered in C1 domains. Existence and uniqueness results are given in a Sobolev space with weights allowing the derivatives of the solutions to blow up near the boundary.
