\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Potential estimates and applications to elliptic equations

Abstract Related Papers Cited by
  • In this paper we prove a potential type estimate for the solutions of some classes of Dirichlet problems associated to certain non divergence structure elliptic equations with smooth datum. As a consequence of our potential bound, we can get an a priori estimate for the solutions of the same kind of Dirichlet problem, but with less regular datum.
    Mathematics Subject Classification: Primary: 35J25, 35B45; Secondary: 31B10.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    R. A. Amanov and F. I. Mamedov, On the regularity of the solutions of degenerate elliptic equations in divergence form, Math. Notes, 83 (2008), 3-13.

    [2]

    M. Borsuk and V. Kondratiev, Elliptic boundary value problems of second order in piecewise smooth domains, North-Holland Mathematical Library, Elsevier, 2006.

    [3]

    F. Chiarenza, M. Frasca and P. Longo, Interior $W^{2,p}$ estimates for nondivergence elliptic equations with discontinuous coefficients, Ricerche Mat., 40 (1991), 149-168.

    [4]

    F. Chiarenza, M. Frasca and P. Longo, $W^{2,p}$-solvability of the Dirichlet problem for nondivergence elliptic equations with $VMO$ coefficients, Trans. Amer. Math. Soc., 336 (1993), 841-853.

    [5]

    G. Di Fazio, $L^p$ estimates for divergence form elliptic equations with discontinuous coefficients, Boll. Unione Mat. Ital. A, 10 (1996), 409-420.

    [6]

    D. Gilbarg andN. S. Trudinger, Elliptic partial differential equations of second order, Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001.

    [7]

    O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and quasilinear elliptic equations, Academic Press, New York-London, 1968.

    [8]

    N. S. Landkof, Foundations of modern potential theory, Die Grundlehren der mathematischen Wissenschaften, Band 180, Springer-Verlag, New York-Heidelberg, 1972.

    [9]

    F. I. Mamedov, Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form, Math. Notes, 53 (1993), 50-58.

    [10]

    A. Maugeri, D. K. Palagachev and L. G. Softova, Elliptic and parabolic equations with discontinuous coefficients, Mathematical Research, 109, Wiley-VCH Verlag Berlin GmbH, Berlin, 2000.

    [11]

    C. Miranda, Sulle equazioni ellittiche del secondo ordine di tipo non variazionale, a coefficienti discontinui, Ann. Mat. Pura Appl., 63 (1963), 353-386.

    [12]

    S. G. Samko, Hypersingular integrals and their applications, Analytical Methods and Special Functions, 5. Taylor & Francis, Ltd., London, 2002.

    [13]

    S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional integrals and derivatives. Theory and applications, translated from the 1987 Russian original, Gordon and Breach Science Publishers, Yverdon, 1993.

    [14]

    E. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J., 1970.

    [15]

    G. Talenti, Sopra una classe di equazioni ellittiche a coefficienti misurabili, Ann. Mat. Pura Appl., 69 (1965), 285-304.

  • 加载中
Open Access Under a Creative Commons license
SHARE

Article Metrics

HTML views() PDF downloads(69) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return