A quasilinear elliptic system with natural growth terms

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• 作者：Lucio Boccardo ; Luigi Orsina…
• 关键词：Nonlinear elliptic systems ; Quasilinear quadratic elliptic equations ; Existence and nonexistence of solutions ; 35J60 ; 35J47 ; 35J57
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：194
• 期：6
• 页码：1733-1750
• 全文大小：512 KB
• 参考文献：1.Benilan, P., Boccardo, L., Gallou毛t, T., Gariepy, R., Pierre, M., Vazquez, J.L.: An \(L^{1}\) -theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa 22, 241鈥?73 (1995)MATH
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  5.Boccardo, L., Leonori, T.: Local properties of solutions of elliptic equations depending on local properties of the data. Methods Appl. Anal. 15, 53鈥?3 (2008)MATH MathSciNet
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  8.Dal Maso, G., Murat, F., Orsina, L., Prignet, A.: Renormalized solutions of elliptic equations with general measure data. Ann. Scuola Norm. Sup. Pisa 28, 741鈥?08 (1999)MATH MathSciNet
  9.de Figueiredo, D.G.: Nonlinear elliptic systems. An. Acad. Bras. Cienc. 72, 453鈥?69 (2000)CrossRef
  10.Giaquinta, M.: Multiple Integral in the Calculus of Variations. Princeton University Press, Princeton (1983)
  11.Landes, R.: On the existence of weak solutions of perturbated systems with critical growth. J. Reine Angew. Math. 393, 21鈥?8 (1989)MATH MathSciNet
  12.Leone, C., Porretta, A.: Entropy solutions for nonlinear elliptic equations in \(L^{1}\) . Nonlinear Anal. 32, 325鈥?34 (1998)MATH MathSciNet CrossRef
  13.Stampacchia, G.: Le probl茅me de Dirichlet pour les quations elliptiques du second ordre 脿 coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15, 189鈥?58 (1965)MATH MathSciNet CrossRef
  
• 作者单位：Lucio Boccardo (1)
  Luigi Orsina (1)
  Jean-Pierre Puel (2)
  
  1. Dipartimento di Matematica, 鈥淪apienza鈥?Universit脿 di Roma, P.le A. Moro 2, 00185, Rome, Italy
  2. Laboratoire de Math茅matiques de Versailles, Universit茅 de Versailles St Quentin, 45 Avenue des Etats Unis, 78035, Versailles Cedex, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891

文摘

In this paper, we prove existence of solutions for an elliptic system of the type $$\begin{aligned} {\left\{ \begin{array}{ll} -\mathrm{div}(a(x,z) \nabla u) = f, &{}\quad \text{ in } \varOmega \text{; } \\ -\mathrm{div}(b(x) \nabla z)+ h(x,z)|\nabla u|^2 = g, &{}\quad \text{ in } \varOmega \text{; } \\ \,u = 0 = z, &{}\quad \text{ on } \partial \varOmega \text{, } \end{array}\right. } \end{aligned}$$