Let be a smooth map and . The -Laplacian is the PDE system
where . This system constitutes the fundamental equation of vectorial calculus of variations in , associated with the model functional
We show that generalised solutions to the system can be characterised in terms of the functional via a set of designated affine variations. For the scalar case N=1, we utilize the theory of viscosity solutions by Crandall-Ishii-Lions. For the vectorial case , we utilize the recently proposed by the author theory of -solutions. Moreover, we extend the result described above to the p-Laplacian, .
Submitted August 10, 2016. Published January 26, 2017.
Math Subject Classifications: 35D99, 35D40, 35J47, 35J47, 35J92, 35J70, 35J99.
Key Words: Infinity-Laplacian; p-Laplacian; generalised solutions; viscosity solutions; calculus of variations in L-infinity; Young measures; fully nonlinear systems.
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| Nikos Katzourakis |
Department of Mathematics and Statistics
University of Reading, Whiteknights, PO Box 220
Reading RG6 6AX, Berkshire, UK
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