Diane L. Denny
Abstract:
This article studies the existence of solutions to the
second-order quasilinear elliptic equation
with the condition
at a certain point
in the domain, which is the 2 or the 3 dimensional torus.
We prove that if the functions a, f, v satisfy
certain conditions, then there exists a unique classical solution.
Applications of our results include stationary heat/diffusion
problems with convection and with a source/sink, when
the value of the solution is known at a certain location.
Submitted April 13, 2010. Published June 18, 2010.
Math Subject Classifications: 35A05.
Key Words: Existence; uniqueness; quasilinear; elliptic.
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Diane L. Denny Department of Mathematics and Statistics Texas A\&M University - Corpus Christi Corpus Christi, TX 78412, USA email: diane.denny@tamucc.edu |
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