Existence of Bounded Solutions for Some Degenerated Quasilinear Elliptic Equations
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We prove the existence of bounded solutions in L ∞ (Ω) of degenerate elliptic boundary value problems of second order in divergence form with natural growth in the gradient. For the Dirichlet problem our results cover also unbounded domains Ω.
KeywordsBoundary Value Problem Dirichlet Problem Unbounded Domain Bound Solution Nonlinear Elliptic Equation
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- 2.L. Boccardo, F. Murat, and J. P. Puel: Existence de solutions faibles pour des equations elliptiques quasilineares à croissance quadratique, in Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar, Vol. IV, edited by M. Brèzis and J. L. Lions, Research Notes in Mathematics, 84, Pitman, London (1983), pp. 19–73.Google Scholar
- 4.L. Boccardo, F. Murat, and J. P. Puel: L ∞ -estimate and existence of a solution for some nonlinear elliptic equations, to appear in SIAM Math. Analysis.Google Scholar
- 5.L. Boccardo and F. Gallouët: Strongly nonlinear elliptic equations having natural growth terms and L -1-data, to appear in Nonlinear Analysis T.M.A.Google Scholar
- 10.A. V. Ivanov and P. Z. Mkrtycjan: On the solvability of the first boundary value problems for certain classes, of degenerating, quasilinear elliptic equations of the second order, in Boundary Value Problems of Mathematical Physics, Vol. X, edited by O. Ladyzenskaja, Proceedings of the Steklov Institute, A.M.S. Providence (1981), issue 2, pp. 11–35.Google Scholar
- 11.C. Miranda: Istituzioni di analisi funzionale lineare, voll. I e II, U.M.I., Gubbio (1978/1979).Google Scholar