Preprint 18/2010

A counter example to weak maximum principles for locally vanishing elliptic operators

Thomas Blesgen and Anja Schlömerkemper

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Submission date: 15. Apr. 2010 (revised version: July 2010)
Pages: 12
Bibtex
MSC-Numbers: 35B50, 35J15, 74B20
Keywords and phrases: Maximum principles, General theory of second order of second-order ell, nonlinear elasticity
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Abstract:
For the validity of the weak maximum principle for classical solutions of elliptic partial differential equations it is sufficient that the coefficient matrix formula6 is non-negative. In this note we consider maximum principles for weak solutions of elliptic partial differential equations in divergence form with bounded coefficients formula8. We demonstrate that the assumption that the coefficient matrix formula6 is positive almost everywhere is essential and cannot be weakened. To this end we give a counter example originating from geometrically linear elasticity.

07.06.2018, 02:12