Geodesic
Continuity of solutions of a nonlinear elliptic equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 1-19

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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: a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasing l:ℝ+ → ℝ+.

DOI : 10.1051/cocv/2011194
Classification : 35J20, 35J25, 35J60
Keywords: nonlinear elliptic equations, continuity of solutions, lower bounded slope condition, Lavrentiev phenomenon 
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     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Bousquet, Pierre. Continuity of solutions of a nonlinear elliptic equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 1-19. doi: 10.1051/cocv/2011194

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