Diane L. Denny
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
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