Nikos Katzourakis
Abstract:
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 email: n.katzourakis@reading.ac.uk |
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