Quasilinear degenerate elliptic variational inequalities with discontinuous coefficients

Salvatore Bonafede

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 1, page 55-61
  • ISSN: 0010-2628

Abstract

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We obtain an existence theorem for the problem (0.1) where the coefficients a i j ( x , s ) satisfy a degenerate ellipticity condition and hypotheses weaker than the continuity with respect to the variable s .

How to cite

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Bonafede, Salvatore. "Quasilinear degenerate elliptic variational inequalities with discontinuous coefficients." Commentationes Mathematicae Universitatis Carolinae 34.1 (1993): 55-61. <http://eudml.org/doc/247527>.

@article{Bonafede1993,
abstract = {We obtain an existence theorem for the problem (0.1) where the coefficients $a_\{ij\}(x,s)$ satisfy a degenerate ellipticity condition and hypotheses weaker than the continuity with respect to the variable $s$.},
author = {Bonafede, Salvatore},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {degenerate elliptic variational inequalities; pseudomonotone operators; existence; weighted Sobolev space},
language = {eng},
number = {1},
pages = {55-61},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quasilinear degenerate elliptic variational inequalities with discontinuous coefficients},
url = {http://eudml.org/doc/247527},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Bonafede, Salvatore
TI - Quasilinear degenerate elliptic variational inequalities with discontinuous coefficients
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 1
SP - 55
EP - 61
AB - We obtain an existence theorem for the problem (0.1) where the coefficients $a_{ij}(x,s)$ satisfy a degenerate ellipticity condition and hypotheses weaker than the continuity with respect to the variable $s$.
LA - eng
KW - degenerate elliptic variational inequalities; pseudomonotone operators; existence; weighted Sobolev space
UR - http://eudml.org/doc/247527
ER -

References

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  2. Boccardo L., Buttazzo G., Quasilinear elliptic equations with discontinuous coefficients, Atti Acc. Lincei Rend. fis. (8), vol. LXXXII (1988), 21-28. MR0999834
  3. Ekeland I., Tenam R., Analyse convexe et problèmes variationnels, Dunod, Gauthier-Villars, 1974. MR0463993
  4. Guglielmino F., Nicolosi F., Sulle W -soluzioni dei problemi al contorno per operatori ellittici degeneri, Ricerche di Matematica, suppl. vol. XXXVI (1987). 
  5. Guglielmino F., Nicolosi F., Teoremi di esistenza per i problemi al contorno relativi alle equazioni ellittiche quasilineari, Ricerche di Matematica 37 (1988), fasc. 1, 157-176. 
  6. Himmelberg C.J., Measurable relations, Fund. Math. 87 (1975), 53-72. (1975) Zbl0296.28003MR0367142
  7. Ladyzhenskaya O.A., Ural'tseva N.N., Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0177.37404MR0244627
  8. Marina M.E., Una diseguaglianza variazionale associata a un operatore ellittico che puó degenerare, Rend. Acc. Naz. Lincei 55 (1973), 149-160. (1973) MR0463672
  9. Murty M.K.V., Stampacchia G., Boundary value problems for some degenerate elliptic operators, Ann. Mat. Pura Appl. 80 (1968), 1-122. (1968) MR0249828
  10. Ricceri B., A remark on quasilinear elliptic variational inequalities with discontinuous coefficients, Rend. Mat. Acc. Lincei s. 9, vol. 1 (1990), 17-19. MR1081821
  11. Troianello G.M., Elliptic Differential Equations and Obstacle Problem, Plenum Press, 1987. 

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