Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data

Pirro Oppezzo; Anna Maria Rossi

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 2, page 415-433
  • ISSN: 0392-4041

Abstract

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We prove the existence of a renormalized solution for a nonlinear non coercive divergence problem with lower order terms and measure data. In a particular case we also give a uniqueness result.

How to cite

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Oppezzo, Pirro, and Rossi, Anna Maria. "Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data." Bollettino dell'Unione Matematica Italiana 6-B.2 (2003): 415-433. <http://eudml.org/doc/195132>.

@article{Oppezzo2003,
abstract = {We prove the existence of a renormalized solution for a nonlinear non coercive divergence problem with lower order terms and measure data. In a particular case we also give a uniqueness result.},
author = {Oppezzo, Pirro, Rossi, Anna Maria},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {415-433},
publisher = {Unione Matematica Italiana},
title = {Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data},
url = {http://eudml.org/doc/195132},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Oppezzo, Pirro
AU - Rossi, Anna Maria
TI - Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/6//
PB - Unione Matematica Italiana
VL - 6-B
IS - 2
SP - 415
EP - 433
AB - We prove the existence of a renormalized solution for a nonlinear non coercive divergence problem with lower order terms and measure data. In a particular case we also give a uniqueness result.
LA - eng
UR - http://eudml.org/doc/195132
ER -

References

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  2. BOCCARDO, L.- GALLOUËT, T.- ORSINA, L.- Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincare Anal. Non Lineaire, 13, no. 5 (1996), 539-551. Zbl0857.35126MR1409661
  3. BOCCARDO, L.- GALLOUËT, T.- ORSINA, L., Existence and nonexistence of solutions for some nonlinear elliptic equations, J. Anal. Math., 73 (1997), 203-223. Zbl0898.35035MR1616410
  4. DAL MASO, G.- MURAT, F.- ORSINA, L.- PRIGNET, A., Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 28, no. 4 (1999), 741-808. Zbl0958.35045MR1760541
  5. DEL VECCHIO, T.- POSTERARO, M. R., Existence and regularity results for nonlinear elliptic equations with measure data, Adv. Differential Equations, 1, no. 5 (1996), 899-917. Zbl0856.35044MR1392010
  6. LERAY, J.- LIONS, J. L., Quelques resultats de Višik sur les problemes elliptiques semilineaires par les methodes de Minty et Browder, Bull. Soc. Math. France, 93 (1965), 97-107. Zbl0132.10502MR194733
  7. MURAT, F., Soluciones renormalizadas de EDP elipticas no lineales, Publications du Laboratoire d'Analyse Numerique n. 93023, Universite Pierre et Marie Curie, Paris (1993). 
  8. OPPEZZI, P.- ROSSI, A. M., Renormalized Solutions for Divergence Problems with L 1 Data, Atti Sem. Mat. Fis. Univ. Modena Suppl. Vol., 46 (1998), 889-914. Zbl0949.35059MR1645761
  9. OPPEZZI, P.- ROSSI, A. M., Unilateral problems with measure data: links and convergence, Differential Integral Equations, 14, no. 9 (2001), 1051-1076. Zbl1034.35057MR1852871
  10. OPPEZZI, P.- ROSSI, A. M., Renormalized Solutions for Equations with Lower Order Terms and Measure Data, preprint n. 411, DIMA, Università di Genova, April 2000. 
  11. PORRETTA, A., Existence for elliptic equations in L 1 having lower order terms with natural growth, Portugal. Math., 57, no. 2 (2000), 179-190. Zbl0963.35068MR1759814

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