Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data
Date
2004-12-07
Authors
Augsburger, Fabien
Hungerbuhler, Norbert
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We study the quasilinear elliptic system
-div σ(x, u, Du) = v(x) + ƒ(x, u) + div g(x, u)
on a bounded domain of ℝn with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source v in a moving and dissolving substance, where the motion is described by g and the dissolution by ƒ. We prove existence of a weak solution of this system under classical regularity, growth, and coercivity conditions for σ, but with only very mild monotonicity assumptions.
Description
Keywords
Young measure, Noninear elliptic systems
Citation
Augsburger, F., & Hungerbühler, N. (2004). Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data. <i>Electronic Journal of Differential Equations, 2004</i>(144), pp. 1-18.
Rights
Attribution 4.0 International