Advanced search
Publication Cover
Communications in Partial Differential Equations Volume 36, 2011 - Issue 10
Submit an article Journal homepage
556
Views
20
CrossRef citations to date
0
Altmetric
Original Articles

Global Regularity of Weak Solutions to Quasilinear Elliptic and Parabolic Equations with Controlled Growth

Hongjie Dong Division of Applied Mathematics, Brown University, Providence, Rhode Island, USACorrespondence[email protected]
&
Doyoon Kim Department of Applied Mathematics, Kyung Hee University, Yongin-si, Republic of Korea
Pages 1750-1777 | Received 31 Jul 2010, Accepted 05 Mar 2011, Published online: 08 Sep 2011
 
Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days

Abstract

We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of BMO functions with small mean oscillations with respect to x.

Mathematics Subject Classification:

Acknowledgement

We would like to thank Dian K. Palagachev for informing us his recent papers [Citation32, Citation33], and the anonymous referees for their helpful comments. H. Dong was partially supported by NSF grant number DMS-0800129.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related Research Data

Global Hölder continuity of weak solutions to quasilinear divergence form elliptic equations
Source: Elsevier BV
L p Regularity and partial Hölder continuity for solutions of second order parabolic systems with strictly controlled growth
Source: Springer Science and Business Media LLC
The boundary regularity of non-linear parabolic systems I
Source: European Mathematical Society - EMS - Publishing House GmbH
Regularity for quasi-linear elliptic systems with discontinuous coefficients
Source: International Press of Boston
Weighted Lorentz estimates for nonlinear elliptic obstacle problems with partially regular nonlinearities
Source: Springer Science and Business Media LLC
Hölder continuity and partial Hölder continuity results forH 1,q-solutions of non-linear elliptic systems with controlled growth
Source: Springer Science and Business Media LLC
Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation
Source: Springer Science and Business Media LLC
BOUNDARY REGULARITY FOR QUASILINEAR ELLIPTIC SYSTEMS
Source: Informa UK Limited
The boundary regularity of non-linear parabolic systems I
Source: Elsevier BV
Quasilinear divergence form elliptic equations in rough domains
Source: Informa UK Limited
Regularity estimates for BMO-weak solutions of quasilinear elliptic equations with inhomogeneous boundary conditions
Source: Springer Science and Business Media LLC
The existence of regular boundary points for non-linear elliptic systems
Source: Walter de Gruyter GmbH
Lp solvability of divergence type parabolic and elliptic systems with partially BMO coefficients
Source: Springer Science and Business Media LLC
Second Order Parabolic Differential Equations
Source: WORLD SCIENTIFIC
Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients
Source: Springer Science and Business Media LLC
Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions
Source: Duke University Press
On the nonlinear parabolic systems in divergence form. Hölder continuity and partial Hölder continuity of the solutions
Source: Springer Science and Business Media LLC
The Lp-integrability of the partial derivatives of A quasiconformal mapping
Source: Institut Mittag-Leffler
Continuity of Solutions of Parabolic and Elliptic Equations
Source: JSTOR
Lp Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems
Source: Hindawi Limited
Lp theory and partial Hölder continuity for quasilinear parabolic systems of higher order with strictly controlled growth
Source: Springer Science and Business Media LLC
A counter-example to the boundary regularity of solutions to elliptic quasilinear systems
Source: Springer Science and Business Media LLC
Elliptic and Parabolic Equations with Discontinuous Coefficients
Source: Wiley

Linking provided by 

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.