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

作者: Juraj Húska

DOI: 10.1016/J.JDE.2006.02.008

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摘要: Abstract We consider the oblique derivative problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on Lipschitz cylinders. derive an optimal elliptic-type Harnack inequality positive solutions of this and use it to show that each solution exponentially dominates any which changes sign all times. several nontrivial applications both exponential estimate derived inequality.

参考文章(13)
E. B. Fabes, M. V. Safonov, Yu Yuan, Behavior near the boundary of positive solutions of second order parabolic equations. II Transactions of the American Mathematical Society. ,vol. 351, pp. 4947- 4961 ,(1999) , 10.1090/S0002-9947-99-02487-3
Janusz Mierczyński, The Principal Spectrum for Linear Nonautonomous Parabolic PDEs of Second Order: Basic Properties☆ Journal of Differential Equations. ,vol. 168, pp. 453- 476 ,(2000) , 10.1006/JDEQ.2000.3893
Peter Poláčik, , On uniqueness of positive entire solutions and other properties of linear parabolic equations Discrete and Continuous Dynamical Systems. ,vol. 12, pp. 13- 26 ,(2004) , 10.3934/DCDS.2005.12.13
Juraj Húska, Peter Poláčik, Mikhail V. Safonov, Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations Annales De L Institut Henri Poincare-analyse Non Lineaire. ,vol. 24, pp. 711- 739 ,(2007) , 10.1016/J.ANIHPC.2006.04.006
Janusz Mierczyński, Wenxian Shen, Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations Journal of Differential Equations. ,vol. 191, pp. 175- 205 ,(2003) , 10.1016/S0022-0396(03)00016-0
Gary M. Lieberman, Pointwise Estimates for Oblique Derivative Problems in Nonsmooth Domains Journal of Differential Equations. ,vol. 173, pp. 178- 211 ,(2001) , 10.1006/JDEQ.2000.3939
Janusz Mierczyński, Globally Positive Solutions of Linear Parabolic PDEs of Second Order with Robin Boundary Conditions Journal of Mathematical Analysis and Applications. ,vol. 209, pp. 47- 59 ,(1997) , 10.1006/JMAA.1997.5323
Dung Le, Hal Smith, Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains Journal of Mathematical Analysis and Applications. ,vol. 275, pp. 208- 221 ,(2002) , 10.1016/S0022-247X(02)00314-1
Santiago Cano-Casanova, Julián López-Gómez, Properties of the Principal Eigenvalues of a General Class of Non-classical Mixed Boundary Value Problems Journal of Differential Equations. ,vol. 178, pp. 123- 211 ,(2002) , 10.1006/JDEQ.2000.4003