Harnack inequality and exponential separation for oblique derivative problems on Lipschitz domains

Journal of Differential Equations

Volumn 226, Issue 2, 2006, Pages 541-557

  Húska, Juraj ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Exponential separation; Harnack inequalities; Positive entire solutions; Spectral gap

Indexed keywords

EID: 33646532424     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.02.008     Document Type: Article

References (13)

1. Cano-Casanova S., and López-Gómez J. Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems. J. Differential Equations 178 (2002) 123-211
2. Fabes E.B., Safonov M.V., and Yuan Y. Behavior near the boundary of positive solutions of second order parabolic equations II. Trans. Amer. Math. Soc. 12 (1999) 4947-4961
3. Húska J., and Poláčik P. The principal Floquet bundle and exponential separation for linear parabolic equations. J. Dynam. Differential Equations 24 (2004) 1312-1330
4. J. Húska, P. Poláčik, M. Safonov, Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press
5. Le D., and Smith H. Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains. J. Math. Anal. Appl. 275 (2002) 208-221
6. Lieberman G.M. Local estimates for subsolutions and supersolutions of oblique derivative problems for general second order elliptic equations. Trans. Amer. Math. Soc. 304 (1987) 343-353
7. Lieberman G.M. Pointwise estimates for oblique derivative problems in nonsmooth domains. J. Differential Equations 173 (2001) 178-211
8. Mierczyński J. Globally positive solutions of linear PDEs of second order with Robin boundary conditions. J. Math. Anal. Appl. 209 (1997) 47-59
9. Mierczyński J. The principal spectrum for linear nonautonomous parabolic PDEs of second order: Basic properties. J. Differential Equations 168 (2000) 453-476
10. Mierczyński J., and Shen W. Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations. J. Differential Equations 191 (2003) 175-205
11. Poláčik P. On uniqueness of positive entire solutions and other properties of linear parabolic equations. Discrete Contin. Dyn. Syst. 12 (2005) 13-26
12. Poláčik P., and Tereščák I. Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. J. Dynam. Differential Equations 5 (1993) 279-303 Erratum in:
13. Poláčik P., and Tereščák I. Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. J. Dynam. Differential Equations 6 1 (1994) 245-246