Abstract
In this paper we obtain sharp Petrovskiĭ criteria for the \(p\)-parabolic equation, both in the degenerate case \(p>2\) and the singular case \(1<p<2\). We also give an example of an irregular boundary point at which there is a barrier, thus showing that regularity cannot be characterized by the existence of just one barrier.
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Acknowledgments
The first two authors were supported by the Swedish Research Council. Part of this research was done while J. B. visited Università di Pavia in 2014, and the paper was completed while U. G. visited Linköping University in 2015. They want to thank these departments for the hospitality.
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Björn, A., Björn, J. & Gianazza, U. The Petrovskiĭ criterion and barriers for degenerate and singular \(p\)-parabolic equations. Math. Ann. 368, 885–904 (2017). https://doi.org/10.1007/s00208-016-1415-0
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DOI: https://doi.org/10.1007/s00208-016-1415-0