Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations

• Autorzy: Cavalheiro A. C
• Języki publikacji: EN

Abstrakty

EN

In this paper we are interested in the existence of solutions for the Dirichlet problem associated with degenerate nonlinear elliptic equations [formula] in the setting of the weighted Sobolev spaces [formula].

Słowa kluczowe

EN

degenerate nonlinear elliptic equations; weighted Sobolev spaces

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2014
• Tom: Vol. 34, no. 1
• Strony: 15--28
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Cavalheiro A. C

• State University of Londrina Department of Mathematics Londrina – PR – Brazil, 86057-970

Bibliografia

• [1] E. Fabes, D. Jerison, C. Kenig, The Wiener test for degenerate elliptic equations, Annals Inst. Fourier 32 (1982), 151–182.
• [2] S. Fucik, O. John, A. Kufner, Function Spaces, Noordhoff International Publ., Leyden, 1977.
• [3] E. Fabes, C. Kenig, R. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. PDEs 7 (1982), 77–116.
• [4] B. Franchi, R. Serapioni, Pointwise estimates for a class of strongly degenerate elliptic operators: a geometrical approch, Ann. Scuola Norm. Sup. Pisa 14 (1987), 527–568.
• [5] J. Garcia-Cuerva, J.L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies 116 (1985).
• [6] J. Heinonen, T. Kilpeläinen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Math. Monographs, Clarendon Press, 1993.
• [7] A. Kufner, Weighted Sobolev Spaces, John Wiley & Sons, 1985.
• [8] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Am. Math. Soc. 165 (1972), 207–226.
• [9] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, São Diego, 1986.
• [10] B.O. Turesson, Nonlinear Potential Theory and Weighted Sobolev Spaces, Lecture Notes in Mathematics, vol. 1736, Springer-Verlag, 2000.
• [11] E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. II/B, Springer--Verlag, 1990.