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Caccioppoli estimates through an anisotropic Picone's identity


Author: Jaroslav Jaroš
Journal: Proc. Amer. Math. Soc. 143 (2015), 1137-1144
MSC (2010): Primary 35J60
DOI: https://doi.org/10.1090/S0002-9939-2014-12294-5
Published electronically: October 17, 2014
MathSciNet review: 3293729
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Abstract: Caccioppoli-type estimates for a class of nonlinear differential operators which include the $ p$-Laplacian and the pseudo $ p$-Laplacian as special cases are obtained by means of the differential identity involving an arbitrary norm in $ \mathbb{R}^n$ which generalizes the well-known multidimensional Picone's formula.


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Additional Information

Jaroslav Jaroš
Affiliation: Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovakia
Email: jaros@fmph.uniba.sk

DOI: https://doi.org/10.1090/S0002-9939-2014-12294-5
Keywords: Picone identity, Caccioppoli inequality
Received by editor(s): March 15, 2013
Received by editor(s) in revised form: May 31, 2013
Published electronically: October 17, 2014
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society