Continuity of solutions of a nonlinear elliptic equation
Université Aix-Marseille 1, LATP UMR6632 3 place Victor Hugo, 13331
Marseille Cedex 3,
Revised: 10 October 2011
We consider a nonlinear elliptic equation of the form div [a(∇u)] + F[u] = 0 on a domain Ω, subject to a Dirichlet boundary condition tru = φ. We do not assume that the higher order term a satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and φ satisfies a one-sided bounded slope condition, or when a is radial: for some increasing l:ℝ+ → ℝ+.
Mathematics Subject Classification: 35J20 / 35J25 / 35J60
Key words: Nonlinear elliptic equations / continuity of solutions / lower bounded slope condition / Lavrentiev phenomenon
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