Advanced Search
Article Contents
Article Contents

Optimal regularity for parabolic Schrödinger operators

Abstract Related Papers Cited by
  • In this paper we study the regularity theory for the parabolic Schrödinger operator $P=\frac{\partial}{\partial t}-\triangle+V$ under optimal conditions. As a corollary we obtain $L^p$-type regularity estimates for such operator.
    Mathematics Subject Classification: 35J10; 35K10.


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

    E. Acerbi and G. Mingione, Gradient estimates for a class of parabolic systems, Duke Math. J., 136 (2007), 285-320.doi: 10.1215/S0012-7094-07-13623-8.


    R. A. Adams and J. J. F. Fournier, "Sobolev Spaces," 2nd edition, Academic Press, New York, 2003.


    A. Benkirane and A. ElmahiAn existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces, Nonlinear Anal., 36 (1999), 11-24. doi: 10.1016/S0362-546X(97)00612-3.


    S. Byun, F. Yao and S. Zhou, Gradient Estimates in Orlicz space for nonlinear elliptic Equations, J. Funct. Anal., 255 (2008), 1851-1873.doi: 10.1016/j.jfa.2008.09.007.


    A. Carbonaro, G. Metafune and C. Spina, Parabolic Schrödinger operators, J. Math. Anal. Appl., 343 (2008), 965-974.doi: 10.1016/j.jmaa.2008.02.010.


    W. Gao and Y. Jiang, $L^p$ estimate for parabolic Schrödinger operator with certain potentials, J. Math. Anal. Appl., 310 (2005), 128-143.doi: 10.1016/j.jmaa.2005.01.049.


    V. Kokilashvili and M. Krbec, "Weighted Inequalities in Lorentz and Orlicz Spaces," World Scientific, 1991.doi: 10.1142/1367.


    G. M. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996.doi: 10.1142/3302.


    W. Orlicz, Üeber eine gewisse Klasse von Räumen vom Typus B, Bull. Int. Acad. Pol. Ser. A, 8 (1932), 207-220.


    M. Rao and Z. Ren, "Applications of Orlicz Spaces," Marcel Dekker Inc., New York, 2000.doi: 10.1201/9780203910863.


    Z. Shen, On the Neumann problem for Schrödinger operators in Lipschitz domains, Indiana Univ. Math. J., 43 (1994), 143-176.doi: 10.1512/iumj.1994.43.43007.


    Z. Shen, $L^p$ estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble), 45 (1995), 513-546.doi: 10.5802/aif.1463.


    E. M. Stein, "Harmonic Analysis," Princeton University Press, Princeton, 1993.


    L. Wang, F. Yao, S. Zhou and H. Jia, Optimal regularity for the poisson equation, Proc. Amer. Math. Soc., 137 (2009), 2037-2047.doi: 10.1090/S0002-9939-09-09805-0.


    F. Yao, Optimal regularity for Schrödinger equations, Nonlinear Analysis, 71 (2009), 5144-5150.doi: 10.1016/j.na.2009.03.081.

  • 加载中

Article Metrics

HTML views() PDF downloads(86) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint