# American Institute of Mathematical Sciences

April  2015, 35(4): 1521-1530. doi: 10.3934/dcds.2015.35.1521

## Strong positivity of continuous supersolutions to parabolic equations with rough boundary data

 1 Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249

Received  June 2013 Revised  May 2014 Published  November 2014

Parabolic equations given on domains with corners are considered. Under very weak assumption on the coefficients, it will be shown that continuous nonnegative supersolutions are strictly positive.
Citation: Dung Le. Strong positivity of continuous supersolutions to parabolic equations with rough boundary data. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1521-1530. doi: 10.3934/dcds.2015.35.1521
##### References:
 [1] R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction Diffusion Equations, Wiley series in mathematical and computational biology, 2003. doi: 10.1002/0470871296. [2] O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, AMS Transl. Monographs, vol. 23, 1968. [3] D. Le and H. Smith, Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains, J. Math. Anal. Appl., 275 (2002), 208-221. doi: 10.1016/S0022-247X(02)00314-1. [4] H. Smith, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys and Monographs, 41. AMS, Providence, RI, 1995.

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##### References:
 [1] R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction Diffusion Equations, Wiley series in mathematical and computational biology, 2003. doi: 10.1002/0470871296. [2] O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, AMS Transl. Monographs, vol. 23, 1968. [3] D. Le and H. Smith, Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains, J. Math. Anal. Appl., 275 (2002), 208-221. doi: 10.1016/S0022-247X(02)00314-1. [4] H. Smith, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys and Monographs, 41. AMS, Providence, RI, 1995.
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