Electron. J. Diff. Eqns., Vol. 2005(2005), No. 46, pp. 18.
Rectifiability of solutions of the
onedimensional pLaplacian
Mervan Pasic
Abstract:
In the recent papers [8] and [10] a class of
Caratheodory functions
rapidly signchanging
near the boundary point
,
has been constructed so that the
equation
in
admits continuous
bounded solutions
whose graphs
do not possess a finite
length. In this paper, the same class of functions
will be given, but with slightly different input data compared to
those from the previous papers, such that the graph
of each solution
is a rectifiable curve in
. Moreover,
there is a positive constant which does not depend on
so that
.
Submitted November 11, 2004. Published April 24, 2005.
Math Subject Classifications: 35J60, 34B15, 28A75.
Key Words: Nonlinear pLaplacian; bounded continuous solutions;
graph; qualitative properties; length; rectifiability.
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Mervan Pasic
Department of Mathematics
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3, 10000 Zagreb, Croatia
email: mervan.pasic@fer.hr 
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