Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients

Lucio Boccardo

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 2, page 357-368
  • ISSN: 0392-4041

Abstract

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This paper dedicated to the memory of Enrico Magenes, concerning a nonlinear Dirichlet problem, follows the previous one ([1]) dedicated to the memory of Guido Stampacchia, concerning a similar linear problem (see [14]).

How to cite

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Boccardo, Lucio. "Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients." Bollettino dell'Unione Matematica Italiana 5.2 (2012): 357-368. <http://eudml.org/doc/290925>.

@article{Boccardo2012,
abstract = {This paper dedicated to the memory of Enrico Magenes, concerning a nonlinear Dirichlet problem, follows the previous one ([1]) dedicated to the memory of Guido Stampacchia, concerning a similar linear problem (see [14]).},
author = {Boccardo, Lucio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {357-368},
publisher = {Unione Matematica Italiana},
title = {Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients},
url = {http://eudml.org/doc/290925},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Boccardo, Lucio
TI - Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/6//
PB - Unione Matematica Italiana
VL - 5
IS - 2
SP - 357
EP - 368
AB - This paper dedicated to the memory of Enrico Magenes, concerning a nonlinear Dirichlet problem, follows the previous one ([1]) dedicated to the memory of Guido Stampacchia, concerning a similar linear problem (see [14]).
LA - eng
UR - http://eudml.org/doc/290925
ER -

References

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  3. BOCCARDO, L. - DALL'AGLIO, A. - ORSINA, L., Existence and regularity results for some elliptic equations with degenerate coercivity. Dedicated to Prof. C. Vinti (Italian) (Perugia, 1996). Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 51-81. MR1645710
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  5. BOCCARDO, L. - GIACHETTI, D., A nonlinear interpolation result with application to the summability of minima of some integral functionals, Discrete and Continuous Dynamical Systems, Series B, 11 (2009), 31-42. Zbl1369.35017MR2461806DOI10.3934/dcdsb.2009.11.31
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  8. BOCCARDO, L. - MURAT, F., Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal TMA, 19 (1992), 581- 597. Zbl0783.35020MR1183665DOI10.1016/0362-546X(92)90023-8
  9. BOCCARDO, L. - MURAT, F. - PUEL, J.-P., Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl., 152 (1988), 183-196. Zbl0687.35042MR980979DOI10.1007/BF01766148
  10. BREZIS, H., Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble), 18 (1968), 115-175. Zbl0169.18602MR270222
  11. BROWDER, F. E., Existence theorems for nonlinear partial differential equations, Proceedings of Symposia in Pure Mathematics, vol. XVI, American Mathematical Society, Providence (1970), 1-60. MR269962
  12. CASADO-DIAZ, J. - MURAT, F. - PORRETTA, A., Uniqueness results for pseudomonotone problems with p > 2 , C. R. Math. Acad. Sci. Paris, 344 (2007), 487-492. Zbl1118.35307MR2324483DOI10.1016/j.crma.2007.02.007
  13. LERAY, J. - LIONS, J. L., Quelques résultats de Višik sur les problèmes elliptiques semi-linéaires par les méthodes de Minty et Browder, Bull. Soc. Math. France, 93 (1965), 97-107. Zbl0132.10502MR194733
  14. MAGENES, E. - STAMPACCHIA, G., I problemi al contorno per le equazioni differenziali di tipo ellittico, Ann. Scuola Norm. Sup. Pisa, 12 (1958), 247-358. MR123818
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