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On elliptic problems with a nonlinearity depending on the gradient

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EN
Abstrakty
EN
We investigate the solvability of the Neumann problem (1.1) involving the non-linearity depending on the gradient. We prove the existence of a solution when the right hand side ƒ of the equation belongs to Lm( Ω) with 1 ≤m <2.
Rocznik
Strony
377--391
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
Bibliografia
  • [1] S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic differential equations satisfying general boundary conditions I, Commun. Pure Appl. Math. 12 (1959), 623–727.
  • [2] B. Abdellaoui, I. Peral, A. Primo, Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equation, Ann. I.H. Poincare, Analyse non lineaire (2007), online.
  • [3] Ph. Benilan, L. Boccardo, Th. Gallouet, R. Gariepy, M. Pierre J.L. Vazquez, An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Sc. Norm. Sup. Pisa 22 (1995) 2, 242–273.
  • [4] L. Boccardo, T. Gallouet, L. Orsina, Existence and nonexistence of solutions for some nonlinear elliptic problems, J. d’Anal. Math. 73 (1997), 203–223.
  • [5] L. Boccardo, F. Murat, J.P. Puel, R´esultats d’existence pour certain problemes elliptiques quasi-lineaires, Ann. Sc. Norm. Sup. Pisa 11 (1984) 2, 213–235.
  • [6] L. Boccardo, F. Murat, J.P. Puel, Existence de solutions non bornees pour certaines equations quasi-lineaires, Portugaliae Math. 41 (1982), 507–534.
  • [7] H. Brezis, W.A. Strauss, Semi-linear second-order elliptic equations in L1, J. Math. Soc. Japan 25 (1973) 4, 565–590.
  • [8] J. Chabrowski, On the Neumann problem with L1 data, Coll. Math. 107 (2007) 2, 301–316.
  • [9] J. Chabrowski, On the existence of solutions of the Dirichlet problem for nonlinear elliptic equations, Rend. Circ. Mat. Palermo 37 (1988), 65–87.
  • [10] T. Gallouet, J.M. Morel, On some linear problems in L1, Bollettino U.M.I. (6) 4-A (1985), 123–131.
  • [11] Sergio Seguria de Leon, Existence and uniqueness for L1 data of some elliptic equations with natural growth, Advances in Diff. Equations 8 (2003) 11, 1377–1408.
  • [12] J.R. Ward Jr, Perturbations with some superlinear growth for a class of second order elliptic boundary value problems, Nonlin. Anal. TMA 6 (1982) 4, 367–374.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0002-0003
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