Some properties of reachable solutions of nonlinear elliptic equations with measure data

Gianni Dal Maso; Annalisa Malusa

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 25, Issue: 1-2, page 375-396
  • ISSN: 0391-173X

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Dal Maso, Gianni, and Malusa, Annalisa. "Some properties of reachable solutions of nonlinear elliptic equations with measure data." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 25.1-2 (1997): 375-396. <http://eudml.org/doc/84293>.

@article{DalMaso1997,
author = {Dal Maso, Gianni, Malusa, Annalisa},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Radon measures},
language = {eng},
number = {1-2},
pages = {375-396},
publisher = {Scuola normale superiore},
title = {Some properties of reachable solutions of nonlinear elliptic equations with measure data},
url = {http://eudml.org/doc/84293},
volume = {25},
year = {1997},
}

TY - JOUR
AU - Dal Maso, Gianni
AU - Malusa, Annalisa
TI - Some properties of reachable solutions of nonlinear elliptic equations with measure data
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 25
IS - 1-2
SP - 375
EP - 396
LA - eng
KW - Radon measures
UR - http://eudml.org/doc/84293
ER -

References

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  1. [1] P. Bgnilan - L. Boccardo - T. Gallouët - R. Gariepy - M. Pierre - J.L. Vasquez, An L 1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci.22 (1995), 241-273. Zbl0866.35037MR1354907
  2. [2] L. Boccardo - T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal.87 (1989), 149-169. Zbl0707.35060MR1025884
  3. [3] L. Boccardo - T. Gallouët, Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations17 (1992), 641-655. Zbl0812.35043MR1163440
  4. [4] L. Boccardo - T. Gallouët - L. Orsina, Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Ist. H. Poincaré Anal. Non Linéaire13 (1996), 539-551. Zbl0857.35126MR1409661
  5. [5] L. Boccarw - F. Murat, A property of nonlinear elliptic equations when the right-hand side is a measure, Potential Anal.3 (1994), 257-263. Zbl0807.35034MR1290666
  6. [6] L. Boccardo - F. Murat, Remarques sur l'homogénéisation de certains problèmes quasilinéaires, Portugaliae Math.41 (1982), 535-562. Zbl0524.35042MR766874
  7. [7] A. Dall'aglio, Approximated solutions of equations with L1 data. Application to the H-convergence of parabolic quasilinear equations, Ann. Mat. Pura Appl.170 (1996), 207-240. Zbl0869.35050MR1441620
  8. [8] G. Dal Maso, On the integral representation of certain local functionals, Ricerche Mat.32 (1983), 85-113. Zbl0543.49001MR740203
  9. [9] G. Dal Maso - F. Murat - L. Orsina - A. Prignet, Definition and existence of renormalized solutions for elliptic equations with general measure data, C. R. Acad. Sci. Paris Sér. I Math.325 (1997). Zbl0887.35057MR1692311
  10. [10] G. Dal Maso - F. Murat - L. Orsina - A. Prignet, Renormalized solutions for elliptic equations with general measure data, to appear. Zbl0887.35057MR1760541
  11. [11] G. Dolzmann - N. Hungerbühler - S. Müller, The p-harmonic system with measure-valued right hand side, Ann. Ist. H. Poincaré Anal. Non Linéaire14 (1997), 353-364. Zbl0879.35052MR1450953
  12. [12] G. Dolzmann - N. Hungerbuhler - S. Müller, Nonlinear elliptic systems with measure-valued right hand side, to appear. Zbl0895.35029
  13. [13] H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969. Zbl0176.00801MR257325
  14. [14] M. Fukushima - K. Sato - S. Taniguchi, On the closable part of pre-Dirichlet forms and the fine support of the underlying measures, Osaka J. Math.28 (1991), 517-535. Zbl0756.60071MR1144471
  15. [15] L. Greco - T. Ivaniec - C. Sbordone, Inverting the p-harmonic operator, Manuscripta Math.92 (1997), 249-258. Zbl0869.35037MR1428651
  16. [16] J. Heinonen - T. Kilpeläinen - O. Martio, Nonlinear potential theory of degenerate elliptic equations, Oxford University Press, Oxford, 1993. Zbl0780.31001MR1207810
  17. [17] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  18. [18] P.L. Lions - F. Murat, Solutions renormalisées d'équations elliptiques non linéaires, to appear. 
  19. [19] W. Littman - G. Stampacchia - H.F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci.17 (1963), 45-79. Zbl0116.30302MR161019
  20. [20] M. Marcus - V.J. Mizel, Nemitsky operators on Sobolev spaces, Arch. Rational Mech. Anal.51 (1973), 347-370. Zbl0266.46029MR348480
  21. [21] A. Prignet, Remarks on the existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat.15 (1995), 321-337. Zbl0843.35127MR1362776
  22. [22] J. Serrin, Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci.18 (1964), 385-397. Zbl0142.37601MR170094
  23. [23] G. Stampacchia, Le problème de Dirichlet pour les èquations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1965), 189-258. Zbl0151.15401MR192177

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