Regularity results for degenerate elliptic systems

Michael Pingen

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 2, page 369-380
  • ISSN: 0294-1449

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Pingen, Michael. "Regularity results for degenerate elliptic systems." Annales de l'I.H.P. Analyse non linéaire 25.2 (2008): 369-380. <http://eudml.org/doc/78794>.

@article{Pingen2008,
author = {Pingen, Michael},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {regularity of weak solutions; degenerate elliptic systems; Harnack inequality; Liouville theorems},
language = {eng},
number = {2},
pages = {369-380},
publisher = {Elsevier},
title = {Regularity results for degenerate elliptic systems},
url = {http://eudml.org/doc/78794},
volume = {25},
year = {2008},
}

TY - JOUR
AU - Pingen, Michael
TI - Regularity results for degenerate elliptic systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 2
SP - 369
EP - 380
LA - eng
KW - regularity of weak solutions; degenerate elliptic systems; Harnack inequality; Liouville theorems
UR - http://eudml.org/doc/78794
ER -

References

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  1. [1] Baldes A., Degenerate elliptic operators, diagonal systems and variational integrals, Manuscripta Math.55 (1986) 467-486. Zbl0616.35039MR836878
  2. [2] Baoyao C., Regularity of weak solutions for a class of degenerate elliptic systems in diagonal form, in: Proc. Asian Math. Conference 1990, World Scientific, Singapore, New Jersey, London, Hongkong, 1992, pp. 51-54. Zbl0940.35509MR1168221
  3. [3] Caffarelli L.A., Regularity theorems for weak solutions of some nonlinear systems, Comm. Pure Appl. Math35 (1982) 833-838. Zbl0496.35035MR673831
  4. [4] Chanillo S., Wheeden R.L., Weighted Poincaré and Sobolev inequalities and estimates for weighted Peano maximal functions, Amer. J. Math.107 (1985) 1191-1226. Zbl0575.42026MR805809
  5. [5] Chanillo S., Wheeden R.L., Harnack's inequality and mean-value inequalities for solutions of degenerate elliptic equations, Comm. Partial Differential Equations11 (1986) 1111-1134. Zbl0634.35035MR847996
  6. [6] Coifman R.R., Fefferman C., Weighted norm inequalities for maximal functions and singular integrals, Studia Math.51 (1974) 241-250. Zbl0291.44007MR358205
  7. [7] Fabes E., Kenig C., Serapioni R., The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations7 (1982) 77-116. Zbl0498.35042MR643158
  8. [8] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, Springer, Berlin, Heidelberg, New York, 1998. Zbl0361.35003
  9. [9] Hildebrandt S., Widman K.O., On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order, Ann. Sc. Norm. Super. PisaIV (1977) 145-178. Zbl0353.35013MR457936
  10. [10] Hildebrandt S., Widman K.O., Sätze vom Liouvilleschen Typ für quasilineare elliptische Gleichungen und Systeme, Nachr. Akad. Wiss. Göttingen II. Math.-Phys. Klasse4 (1979) 41-59. Zbl0426.35037MR568802
  11. [11] M. Meier, On quasilinear elliptic systems with quadratic growth, preprint 1984. MR742430
  12. [12] Muckenhoupt B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc.165 (1972) 207-226. Zbl0236.26016MR293384
  13. [13] Muckenhoupt B., The equivalence of two conditions for weight functions, Studia Math.49 (1974) 101-106. Zbl0243.44003MR350297
  14. [14] Muckenhoupt B., Wheeden R.L., Weighted bounded mean oscillation and the Hilbert transform, Studia Math.54 (1976) 221-237. Zbl0318.26014MR399741
  15. [15] M. Pingen, Zur Regularitätstheorie elliptischer Systeme und harmonischer Abbildungen, Thesis, University of Duisburg-Essen, 2006. 
  16. [16] Trudinger N.S., On the regularity of generalized solutions of linear non-uniformly elliptic equations, Arch. Rat. Mech. Anal.42 (1971) 51-62. Zbl0218.35035MR344656
  17. [17] Wiegner M., Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme, Math. Z.147 (1976) 21-28. Zbl0316.35039MR407430
  18. [18] Wiegner M., A-priori Schranken für Lösungen gewisser elliptischer Systems, Manuscripta Math.18 (1976) 279-297. Zbl0323.35032MR402272

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