Electron. J. Diff. Equ., Vol. 2010(2010), No. 82, pp. 1-21.

Existence and uniqueness of classical solutions to second-order quasilinear elliptic equations

Diane L. Denny

This article studies the existence of solutions to the second-order quasilinear elliptic equation
 -\nabla \cdot(a(u) \nabla u) + v\cdot \nabla u=f
with the condition $u(x_0)=u_0$ 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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