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Optimal regularity for parabolic Schrödinger operators
1. | Department of Mathematics, Shanghai University, Shanghai 200444, China |
References:
[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. |
[2] |
R. A. Adams and J. J. F. Fournier, "Sobolev Spaces," 2nd edition, Academic Press, New York, 2003. |
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A. Benkirane and A. Elmahi, An existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces,, \emph{ \textcolor{blue}{in Orlicz spaces}, ().
doi: 10.1016/S0362-546X(97)00612-3. |
[4] |
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. |
[5] |
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. |
[6] |
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. |
[7] |
V. Kokilashvili and M. Krbec, "Weighted Inequalities in Lorentz and Orlicz Spaces," World Scientific, 1991.
doi: 10.1142/1367. |
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G. M. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
doi: 10.1142/3302. |
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W. Orlicz, Üeber eine gewisse Klasse von Räumen vom Typus B, Bull. Int. Acad. Pol. Ser. A, 8 (1932), 207-220. |
[10] |
M. Rao and Z. Ren, "Applications of Orlicz Spaces," Marcel Dekker Inc., New York, 2000.
doi: 10.1201/9780203910863. |
[11] |
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. |
[12] |
Z. Shen, $L^p$ estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble), 45 (1995), 513-546.
doi: 10.5802/aif.1463. |
[13] |
E. M. Stein, "Harmonic Analysis," Princeton University Press, Princeton, 1993. |
[14] |
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. |
[15] |
F. Yao, Optimal regularity for Schrödinger equations, Nonlinear Analysis, 71 (2009), 5144-5150.
doi: 10.1016/j.na.2009.03.081. |
show all references
References:
[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. |
[2] |
R. A. Adams and J. J. F. Fournier, "Sobolev Spaces," 2nd edition, Academic Press, New York, 2003. |
[3] |
A. Benkirane and A. Elmahi, An existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces,, \emph{ \textcolor{blue}{in Orlicz spaces}, ().
doi: 10.1016/S0362-546X(97)00612-3. |
[4] |
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. |
[5] |
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. |
[6] |
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. |
[7] |
V. Kokilashvili and M. Krbec, "Weighted Inequalities in Lorentz and Orlicz Spaces," World Scientific, 1991.
doi: 10.1142/1367. |
[8] |
G. M. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
doi: 10.1142/3302. |
[9] |
W. Orlicz, Üeber eine gewisse Klasse von Räumen vom Typus B, Bull. Int. Acad. Pol. Ser. A, 8 (1932), 207-220. |
[10] |
M. Rao and Z. Ren, "Applications of Orlicz Spaces," Marcel Dekker Inc., New York, 2000.
doi: 10.1201/9780203910863. |
[11] |
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. |
[12] |
Z. Shen, $L^p$ estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble), 45 (1995), 513-546.
doi: 10.5802/aif.1463. |
[13] |
E. M. Stein, "Harmonic Analysis," Princeton University Press, Princeton, 1993. |
[14] |
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. |
[15] |
F. Yao, Optimal regularity for Schrödinger equations, Nonlinear Analysis, 71 (2009), 5144-5150.
doi: 10.1016/j.na.2009.03.081. |
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