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Applicable Analysis
An International Journal
Volume 82, 2003 - Issue 2
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Original Articles

Summability of Solutions of Dirichlet Problem for a Class of Degenerate Nonlinear High-order Equations

Alexander Kovalevsky Institute of Applied Mathematics and Mechanics, Rosa Luxemburg St. 74, Donetsk, 83114, Ukraine
&
Francesco Nicolosi Dipartimento di Matematica e Informatica, Città Universitaria, Viale A. Doria 6, Catania, 95125, Italia
Pages 93-101 | Published online: 09 Sep 2010

  • Bénilan , Ph. , Boccardo , L. , Gallouët , T. , Gariepy , R. , Pierre , M. and Vazquez , J.L. 1995 . An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations . Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 22 : 241 – 273 .
  • Boccardo , L. and Gallouët , T. 1989 . Non-linear elliptic and parabolic equations involving measure data . J. Funct. Anal. , 87 : 149 – 169 .
  • Boccardo , L. and Gallouët , T. 1992 . Nonlinear elliptic equations with right hand side measures . Comm. Partial Differential Equations , 17 : 641 – 655 .
  • Kovalevsky , A. 1999 . Entropy solutions of Dirichlet problem for a class of nonlinear elliptic fourth order equations with L1-data . Nonlinear Boundary Value Problems , 9 : 46 – 54 .
  • Kovalevsky , A.A. 2001 . Entropy solutions of the Dirichlet problem for a class of nonlinear elliptic fourth-order equations with right-hand sides in L1 . Izvestiya: Mathematics , 65 : 231 – 283 .
  • Kovalevsky , A. 2001 . Integrability of solutions of nonlinear elliptic equations with right-hand sides from classes close to L1 . Math. Notes , 70 : 337 – 346 .
  • A.A. Kovalevsky. On summability of entropy solutions of Dirichlet problem for a class of nonlinear elliptic fourth-order equation, to appear.
  • Kovalevsky , A.A. and Nicolosi , F. 2002 . Entropy solutions of Dirichlet problem for a class of degenerate anisotropic fourth-order equations with L1-right-hand sides . Nonlinear Analysis, Theory Methods and Applications , 50 : 581 – 619 .
  • Kovalevsky , A. and Nicolosi , F. 2001 . Solvability of Dirichlet problem for a class of degenerate nonlinear high-order equations with L1-data . Nonlinear Analysis, Theory Methods and Applications , 47 : 435 – 446 .
  • Lions , J.L. 1969 . Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires , Paris : Dunod, Gauthier-Villars .

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