101
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Hölder continuous Young measure solutions to coercive non-monotone parabolic systems in two space dimensions

&
Pages 67-84 | Received 02 Feb 2010, Accepted 21 Feb 2010, Published online: 06 Jan 2011

References

  • J. Frehse, and M. Specovius-Neugebauer, Morrey estimates and Hölder continuity for solutions to parabolic equations with entropy inequalities, J. Reine Angew. Math. 638 (2010), pp. 169–188.
  • J. Stará and O. John, On some regularity and nonregularity results for solutions to parabolic systems, Matematiche (Catania) 55 (2000), pp. 145–163.
  • Wolf , J . 1999 . “ Hölder continuity of weak solutions to certain nonlinear parabolic systems in two space dimensions ” . In in Applied Nonlinear Analysis , Edited by: Sequeira , A . 531 – 546 . New York : Kluwer/Plenum .
  • J. Naumann and J. Wolf, Hölder continuity of weak solutions to parabolic systems with controlled growth non-linearities (two spatial dimensions), Matematiche (Catania) 55 (2000), pp. 125–144.
  • O.A. Ladyženskaja, V.A. Solonnikov, N.N. Ural'ceva, Linear and quasilinear equations of parabolic type. (Russian) Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23 American Mathematical Society, Providence, R.I
  • Müller , S , Rieger , MO and Šverǎk , V . 2005 . Parabolic systems with nowhere smooth solutions . Arch. Ration. Mech. Anal. , 177 : 1 – 20 .
  • Slemrod , M . 1991 . Dynamics of measure valued solutions to a backward-forward heat equation . J. Dyn. Differ. Equ. , 3 : 1 – 28 .
  • Demoulini , S . 1996 . Young measure solutions for a nonlinear parabolic equation of forward-backward type . SIAM J. Math. Anal. , 27 : 376 – 403 .
  • Brenner , SC and Scott , LR . 2008 . “ The mathematical theory of finite element methods ” . In 3rd ed., Texts in Applied Mathematics , Vol. 15 , New York : Springer-Verlag .
  • Widmann , KO . 1971 . Hölder continuity of solutions of elliptic systems . Manuscripta Math. , 5 : 299 – 308 .
  • Frehse , J . 1973 . “ Morrey space methods in the theory of elliptic difference equations ” . In in Numerische, Insbesondere Approximationstheoretische Behandlung von Funktionalgleichungen (Tagung, Math. Forschungsinst., Oberwolfach, 1972), Lecture Notes in Mathematics , Vol. 333 , 96 – 117 . Berlin : Springer .
  • Frehse , J and Rannacher , R . 1975 . “ Eine L1-Fehlerabschätzung für discrete Grundlösungen in der Methode der finiten Elemente ” . In Finite Elemente , Univ. Bonn, Bonn : Tagung . Bonn. Math. Schrift, No. 89, pp. 92–114
  • Frehse , J . 1982 . Capacity methods in the theory of partial differential equations . Jahresber. Deutsch. Math. – Verein. , 84 : 1 – 44 .
  • Stummel , F . 1966 . Über die Differenzenapproximation des Dirichletproblems für eine lineare elliptische Differentialgleichung zweiter Ordnung . Math. Ann. , 163 : 321 – 339 .
  • S. Agmon, Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, Vol. 2, D. Van Nostrand Co., Princeton, N.J., Toronto, London, 1965 (Prepared for publication by B. Frank Jones Jr with the assistance of George W. Batten Jr).
  • Kinderlehrer , D and Pedregal , P . 1992 . Weak convergence of integrands and the Young measure representation . SIAM J. Math. Anal. , 23 : 1 – 19 .
  • Ball , JM . 1989 . “ A version of the fundamental theorem for Young measures ” . In in PDEs and Continuum Models of Phase Transitions (Nice, 1988) , 207 – 215 . Berlin : Springer .

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:

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:

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.