The p-harmonic system with measure-valued right hand side

Georg Dolzmann; Norbert Hungerbühler; Stefan Müller

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 3, page 353-364
  • ISSN: 0294-1449

How to cite


Dolzmann, Georg, Hungerbühler, Norbert, and Müller, Stefan. "The p-harmonic system with measure-valued right hand side." Annales de l'I.H.P. Analyse non linéaire 14.3 (1997): 353-364. <>.

author = {Dolzmann, Georg, Hungerbühler, Norbert, Müller, Stefan},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {-Laplacian; Radon measure; Lorentz space estimate; regularized test function; localization argument},
language = {eng},
number = {3},
pages = {353-364},
publisher = {Gauthier-Villars},
title = {The p-harmonic system with measure-valued right hand side},
url = {},
volume = {14},
year = {1997},

AU - Dolzmann, Georg
AU - Hungerbühler, Norbert
AU - Müller, Stefan
TI - The p-harmonic system with measure-valued right hand side
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 3
SP - 353
EP - 364
LA - eng
KW - -Laplacian; Radon measure; Lorentz space estimate; regularized test function; localization argument
UR -
ER -


  1. [1] P. Bénilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre and J.L. Vazquez, An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Vol. 22, 1995, pp. 241-273. Zbl0866.35037MR1354907
  2. [2] L. Boccardo and T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal., Vol. 87, 1989, pp. 149-169. Zbl0707.35060MR1025884
  3. [3] L. Boccardo and T. Gallouët, Nonlinear elliptic equations with right-hand side measures. Comm. Part. Diff. Eqn., Vol. 17, 1992, pp. 641-655. Zbl0812.35043MR1163440
  4. [4] L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Nonlinear Anal., Vol. 19, 1992, pp. 581-597. Zbl0783.35020MR1183665
  5. [5] Y. Chen, M.-C. Hong and N. Hungerbühler, Heat flow of p-harmonic maps with values into spheres. Math. Z., Vol. 215, 1994, pp. 25-35. Zbl0793.53049MR1254812
  6. [6] E. Dibenedetto and J. Manfredi, On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems. Am. J. Math., Vol. 115, 1993, pp. 1107-1134. Zbl0805.35037MR1246185
  7. [7] L.C. Evans, Weak convergence methods for nonlinear partial differential equations. CBMS Regional Conf. Ser. in Math., No. 74, Am. Math. Soc., Providence, RI, 1990. Zbl0698.35004MR1034481
  8. [8] L.C. Evans and R. Gariepy, Measure theory and fine properties of functions. CRC Press, Boca Raton (etc.), 1992. Zbl0804.28001MR1158660
  9. [9] Fuchs , M.The Green-matrix for elliptic systems which satisfy the Legendre-Hadamard condition. Manuscr. Math., Vol. 46, 1984, pp. 97-115. Zbl0552.35025MR735516
  10. [10] M. Fuchs, The Green matrix for strongly elliptic systems of second order with continuous coefficients. Z. Anal. Anwend., Vol. 5 (6), 1986, pp. 507-531. Zbl0634.35023MR894243
  11. [11] M. Fuchs, The blow-up of p-harmonic maps. Manuscr. Math., Vol. 81, 1993, pp. 89-94. Zbl0794.58012MR1247590
  12. [12] M. Fuchs and J. Reuling, Non-linear elliptic systems involving measure data. Rend. Math. Appl., Vol. 15, 1995, pp. 311-319. Zbl0838.35133MR1339247
  13. [13] M. Grüter and K.-O. Widman, The Green function for uniformly elliptic equations. Manuscr. Math., Vol. 37, 1982, pp. 303-342. Zbl0485.35031MR657523
  14. [14] P.L. Lions and F. Murat, Solutions renormalisées d'equations elliptiques (to appear). 
  15. [15] S. Müller, Det = det. A remark on the distributional determinant. C.R. Acad. Sci., Paris, Sér. I, Vol. 311, 1990, pp. 13-17. Zbl0717.46033MR1062920
  16. [16] F. Murat, Équations elliptiques non linéaires avec second membre L1 ou mesure. Preprint. 
  17. [17] F. Murat, Soluciones renormalizadas de EDP elipticas no lineales. Publications du Laboratoire d'Analyse Numérique R93023, 1993. 
  18. [181 J.M. Rakotoson, Generalized solutions in a new type of sets for problems with measure data. Differ. Integral Eqn., Vol. 6, 1993, pp. 27-36. Zbl0780.35047MR1190163
  19. [19] G. Talenti, Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces. Ann. Mat. Pura Appl., IV. Ser., Vol. 120, 1979, pp. 159-184. Zbl0419.35041MR551065

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.