Research profile of Xiao Zhong

Math Reviews of papers (requires MathSciNet license)

Research Interests

Nonlinear Potential Theory
Partial Differential Equations
Geometric Function Theory

Publications and Preprints

1. A note on the number of positive solutions of some nonlinear elliptic problems, Nonlinear Anal. 27 (1996), 1095--1108. (Joint with D. Cao and G. Li)

2. Multiplicity of positive solutions for semilinear elliptic equations involving the critical Sobolev exponents, Nonlinear Anal. 29 (1997), 461--483.(Joint with D. Cao)

3. On nonhomogeneous quasilinear elliptic equations, Ann. Acad. Sci. Fenn. Math. Diss. 117 (1998), 1--46.

4. Removable sets for continuous solutions of quasilinear elliptic equations, Proc. Amer. Math. Soc. 130 (2002), 1681--1688. (Joint with T. Kilpeläinen)

5. Hardy's inequality and the size of the boundary, Proc. Amer. Math. Soc. 131 (2002), 1151--1158. (Joint with P. Koskela)

6. Minimal assumption for the integrability of the Jacobian, Ricerche di Matematica 2 (2002), 297--311. (Joint with P. Koskela)

7. Growth of entire A-subharmonic functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 28 (2003), 181--192. (Joint with T. Kilpeläinen)

8. Quasiconvex functions and $k$-Hessian, Arch. Ration. Mech. Anal. 168 (2003), 245--252. (Joint with D. Faraco)

9. Mappings of finite distortion: sharp Orlicz conditions, Revista Mat. Iberoamericana 19 (2003), no.3, 857--872. (Joint with J. Kauhanen, P. Koskela, J. Mal\'y and J. Onninen)

10. Mappings of finite distortion: the degree of regularity, Adv. Math. 190 (2005), 300-318. (Joint with D. Faraco and P. Koskela)

11. A lemma on the higher integrability of functions with applications to the regularity theory of two-dimensional generalized Newtonian fluids, Manuscripta Math. 116 (2005), no. 2, 135--156. (Joint with M. Bildhauer and M. Fuchs)

12. A note on mappings of finite distortion: The sharp modulus of continuity, Michigan Math. J. 53 (2005), no. 2, 329--335. (Joint with J. Onninen)

13. Geometric rigidity of conformal matrices, Ann. Sc. Norm. Super. Pisa Cl. Sc. (5) Vol. IV (2005), 557--585. (Joint with D. Faraco)

14. A short proof of the self-improving regularity of Quasiregular mappings, Proc. Amer. Math. Soc. 134 (2006), no. 1, 187--192. (Joint with D. Faraco)

15. On strong solutions of the differential equations modelling the steady flow of certain incompressible generalized Newtonian fluids, Algebra i Analiz 18 (2006), no. 2, 1--23. (Joint with M. Bildhauer and M. Fuchs)

16. The Poincar\'e inequality is an open ended condition, Ann. of Math. 167 (2008), 575--599. (Joint with S. Keith)

17. Mappings of finite distortion: Reverse inequalities for the Jacobian, J. Geom. Anal. 17 (2007), no. 2, 253--274. (Joint with S. Hencl and P. Koskela)

18. Variational integrals with a wide range of anisotropy, Algebra i Analiz 18 (2006), no. 5, 46--71. (Joint with M. Bildhauer and M. Fuchs)

19. Boundary Harnack principle for $p$-harmonic functions in smooth Euclidean domains, Potential Anal. 26 (2007), no. 3, 281--301 (Joint with H. Aikawa, T. Kilpeläinen and N. Shanmugalingam)

20. Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sc. (5) 6 (2007), 103--116. (Joint with J. Onninen)

21. Mappings of finite distortion: new proof of discreteness and openness, Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), no. 5, 1097--1102. (Joint with J. Onninen)

22. Maximal regularity via reverse Holder inequalities for elliptic systems of $n$-Laplace type involving measures, Ark. Mat. 46 (2008), no. 1, 77--93. (Joint with T. Kilpeläinen and N. Shanmugalingam)

23. A regularity theory for scalar local minimizers of splitting-type variational integrals, Ann. Sc. Norm. Super. Pisa Cl. Sc. (5) 6 (2007), 385--404. (Joint with M. Bildhauer and M. Fuchs)

24. Growth estimates through scaling for quasilinear partial differential equations, Ann. Acad. Sci. Fenn. Ser. A I Math. 32 (2007), 595--599. (Joint with T. Kilpeläinen and H. Shahgholian)

25. Beltrami equations with coefficient in the Sobolev space W^{1,p}, Publ. Mat. 53 (2009), no. 1, 19--230. (Joint with A. Clop, D. Faraco, J. Mateu and J. Orobitg)

26. A new approach to interior regularity of elliptic systems with quadratic Jacobian structure in dimension two, Manuscripta Math. 127 (2008), no.1, 121--135. (Joint with P. Hajlasz and P. Strzelecki)

27. A note on the Muckenhoupt weights, submitted, 2007 (Joint with S. Keith)

28. Gradient regularity for elliptic equations in the Heisenberg group, Adv. Math. 222 (2009), no. 1, 62--129. (Joint with G. Mingione and A. Zatorska-Goldstein)
29. Discontinuous solutions of linear, degenerate elliptic equations, J. Math. Pures Appl. (9) 90 (2008), 31--41.
30. Bonnesen's inequality for John domains in R^n, preprint, 2010. (with K. Rajala)