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

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: $a\left(\xi \right)=\frac{l\left(|\xi |\right)}{|\xi |}\xi$ for some increasing l:ℝ+ → ℝ+.

DOI : https://doi.org/10.1051/cocv/2011194
Classification : 35J20,  35J25,  35J60
Mots clés : nonlinear elliptic equations, continuity of solutions, lower bounded slope condition, Lavrentiev phenomenon
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title = {Continuity of solutions of a nonlinear elliptic equation},
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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. http://www.numdam.org/articles/10.1051/cocv/2011194/

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