Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data

Lucio Boccardo; Thierry Gallouët; Luigi Orsina

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 5, page 539-551
  • ISSN: 0294-1449

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Boccardo, Lucio, Gallouët, Thierry, and Orsina, Luigi. "Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data." Annales de l'I.H.P. Analyse non linéaire 13.5 (1996): 539-551. <http://eudml.org/doc/78391>.

@article{Boccardo1996,
author = {Boccardo, Lucio, Gallouët, Thierry, Orsina, Luigi},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {-capacity; decomposition theorem; existence and uniqueness; entropy solutions},
language = {eng},
number = {5},
pages = {539-551},
publisher = {Gauthier-Villars},
title = {Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data},
url = {http://eudml.org/doc/78391},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Boccardo, Lucio
AU - Gallouët, Thierry
AU - Orsina, Luigi
TI - Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 5
SP - 539
EP - 551
LA - eng
KW - -capacity; decomposition theorem; existence and uniqueness; entropy solutions
UR - http://eudml.org/doc/78391
ER -

References

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  1. [1] P. Benilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre and J.L. Vazquez, An L1 theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa, Vol. 22, n. 2, 1995, pp. 240-273. 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. Partial Differential Equations, Vol. 17, n. 3&4, 1992, pp. 641-655. Zbl0812.35043
  4. [4] H. Brezis, Some variational problems of the Thomas-Fermi type, in Variational inequalities and complementarity problems, Cottle, Gianessi, and Lions eds., Wiley, New York, 1980, pp. 53-73. Zbl0643.35108MR578739
  5. [5] H. Brezis and W. Strauss, Semi-linear second-order elliptic equations in L1, J. Math. Soc. Japan, Vol. 25, n. 4, 1973, pp. 565-590. Zbl0278.35041MR336050
  6. [6] A. Dall'aglio, Approximated solutions of equations with L1 data. Application to the H-convergence of parabolic quasi-linear equations, Ann. Mat. Pura Appl., Vol. 170, 1996, pp. 207-240. Zbl0869.35050MR1441620
  7. [7] G. Dal Maso, On the integral representation of certain local functionals, Ricerche Mat., Vol. 22, 1983, pp. 85-113. Zbl0543.49001MR740203
  8. [8] G. Dal Maso, Personal communication. 
  9. [9] M. Fukushima, K. Sato and S. Taniguchi, On the closable part of pre-Dirichlet forms and the fine supports of underlying measures, Osaka J. Math., Vol. 28, 1991, pp. 517-535. Zbl0756.60071MR1144471
  10. [10] T. Gallouët and J.M. Morel, Resolution of a semilinear equation in L1, Proc. Roy. Soc. Edinburgh, Vol. 96, 1984, pp. 275-288. Zbl0573.35030MR760776
  11. [11] J. Leray and J.L. Lions, Quelques résultats de Višik sur les problèmes elliptiques semi-linéaires par les méthodes de Minty et Browder, Bull. Soc. Math. France, Vol. 93, 1965, pp. 97-107. Zbl0132.10502MR194733
  12. [12] A. Prignet, Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat., Vol. 15, 1995, pp. 321-337. Zbl0843.35127MR1362776
  13. [13] J. Serrin, Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa, Vol. 18, 1964, pp. 385-387. Zbl0142.37601MR170094
  14. [14] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, (Grenoble), Vol. 15, n. 1, 1965, pp. 189-258. Zbl0151.15401MR192177

Citations in EuDML Documents

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  1. François Murat, Équations elliptiques non linéaires monotones avec un deuxième membre L 1 ou mesure
  2. Alano Ancona, Sur une question de H. Brezis, M. Marcus et A. C. Ponce
  3. Chiara Leone, Stability results for obstacle problems with measure data
  4. Pirro Oppezzo, Anna Maria Rossi, Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data
  5. M. F. Betta, A. Mercaldo, F. Murat, M. M. Porzio, Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in L 1 ( Ω )
  6. Nathalie Grenon, Existence results for semilinear elliptic equations with small measure data
  7. Gianni Dal Maso, Annalisa Malusa, Some properties of reachable solutions of nonlinear elliptic equations with measure data
  8. Tero Kilpeläinen, Problems involving p -Laplacian type equations and measures
  9. A. Porretta, Absorption effects for some elliptic equations with singularities
  10. M. F. Betta, A. Mercaldo, F. Murat, M. M. Porzio, Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in  (Ω)

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