Zhongwei SHEN's Home Page

Zhongwei Shen

Professor and Chair of Mathematics

B.S. Peking University, 1982.
Ph.D. University of Chicago, 1989.

Ralph E. and Norma L. Edwards Research Professor

Department of Mathematics
University of Kentucky
Lexington, KY 40506-0027
Phone: (859) 257-6794
Fax: (859) 257-4078
Email: zshen2@email.uky.edu
Office:
721 Patterson Office Tower

(a list of Shen's publications on Math Review)

Research Papers Since 1995

The Neumann Problem in L^p on Lipschitz and Convex Domains, with Aekyoung Shin Kim, J. of Functional Analysis 255, pp.1817-1830 (2008).
W^{1,p} Estimates for Elliptic Homogenization Problems in Nonsmooth Domains, pdf file, Indiana Univ. Math. J. 57(5), pp.2283-2298 (2008).
Uniform Sobolev Inequalities and Absolute Continuity of Periodic Operators, with Peihao Zhao, Transactions of AMS 360 (2008), pp.1741-1758.
The $L^p$ Boundary Value Problems on Lipschitz Domains, pdf file, Adv. Math. 216 (2007), pp.212-254.
A Relationship between the Dirichlet and Regularity Problems for Elliptic Equations, Math. Res. Letters 14 (2007), pp.205-213
On Estimates of Biharmonic Functions on Lipschitz and Convex Domains, J. Geometric Analysis 16 (2006), pp.721-734
Necessary and Sufficient Conditions for the Solvability of the Lp Dirichlet Problem on Lipschitz Domains, Math. Ann. 336 (2006), pp.697-725
The L^p Dirichlet Problem for Elliptic Systems on Lipschitz Domains, Math. Research Letters 13 (2006), pp.143-159
Weighted Estimates for Elliptic Systems in Lipschitz Domains, Indiana Univ. Math. J. 55 (2006), pp.1135-1154
Bounds of Riesz Transforms on L^p Spaces for Second Order Elliptic Operators, Ann. Inst. Fourier (Grenoble) 55 (2005), pp.173-197
Weighted Estimates in L^2 for Laplace's Equation in Lipschitz Domains, Trans. Amer. Math. Soc. 357 (2005), pp.2843-2870
On the Robin Boundary Condition for Laplace's Equation in Lipschitz Domain, with Loredana Lanzani, Comm. Partial Diff. Eqs. 29 (2004), pp.91-109
The Spectrum of Schrodinger Operators with Positive Potentials in Riemannian Manifolds, Proc. Amer. Math. Soc. 131 (2003), pp.3447-3456
Boundary Value Problems in Morrey Spaces for Elliptic Systems in Lipschitz Domains, Amer. J. Math. 125 (2003), pp.1079-1115
On the Bethe-Sommerfeld Conjecture for Higher-Order Elliptic Operators, Math. Ann. 326 (2003), pp.19-41
The Periodic Schrodinger Operators with Potentials in the Morrey Class, J. Functional Analysis 193 (2002), pp.3145-345
Absolute Continuity of Periodic Schrodinger Operators with Potentials in the Kato Class, Illinois J. Math. (2001) 45, 873-893
On Absolute Continuity of the Periodic Schr\"odinger Operators, International Math. Research Notices 2001 (1) (2001), pp.1-31
On the Dimension of the Attractor for the Non-Homogeneous Navier-Stokes Equations in Non-Smooth Domains, with R. Brown and P. Perry, Indiana Univ. Math. J. 49 (2000), pp.81-112
On Fundamental Solutions of Generalized Schr\Odinger Operators, J. Functional Analysis 167 (1999), pp.521-564
On Moments of Negative Eigenvalues for the Pauli Operator, J. Diff. Eqs. 149 (1998), pp.292-327
Regularity of Solutions to a Contact Problem, with R. Brown and P. Shi, Trans. Amer. Math. Soc. 350 (1998), pp.4053-4063
On Bounds of $N(\lambda)$ for a Magnetic Schr\"odinger Operator, Duke Math. J. 94 (1998), pp.479-507
The Additive Turbulent Decomposition for the Two-Dimensional Incompressible Navier-Stokes Equations: Convergence Theorems and Error Estimates, with R. Brown and P. Perry, SIAM J. Appl. Math. 59 (1998), pp.139-155
On the Number of Negative Eigenvalues for a Schrodinger Operator with Magnetic Field, Comm. Math. Phys. 182 (1996), pp.637-660
Estimates in $L^p$ for Magnetic Schrodinger Operators, Indiana Univ. Math. J. 45 (1996), pp.817-841
Eigenvalue Asymptotics and Exponential Decay of Eigenfunctions for Schrodinger Operators with Magnetic Fields, Trans. Amer. Math. Soc. 348 (1996), pp.4465-4488
Estimates for the Stokes Operator in Lipschitz Domains, with R. Brown, Indiana Univ. Math. J. 44 (1995), pp.1183-1206
$L^p$ Estimates for Schrodinger Operators with Certain Potentials, Ann. Inst. Fourier (Grenoble) 44 (1995), pp.513-546
Resolvent Estimates in $L^p$ for Elliptic Systems in Lipschitz Domains, J. Functional Analysis 133 (1995), pp.224-251
A Note on the Dirichlet Problem for the Stokes System in Lipschitz Domains, Proc. Amer. Math. Soc. 123 (1995), pp.801-811

Zhongwei Shen

Professor and Chair of Mathematics

Research Papers Since 1995

Courses Taught at the University of Kentucky