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+.
Keywords: nonlinear elliptic equations, continuity of solutions, lower bounded slope condition, Lavrentiev phenomenon
@article{COCV_2013__19_1_1_0, author = {Bousquet, Pierre}, title = {Continuity of solutions of a nonlinear elliptic equation}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1--19}, publisher = {EDP-Sciences}, volume = {19}, number = {1}, year = {2013}, doi = {10.1051/cocv/2011194}, mrnumber = {3023057}, zbl = {1271.35028}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2011194/} }
TY - JOUR AU - Bousquet, Pierre TI - Continuity of solutions of a nonlinear elliptic equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1 EP - 19 VL - 19 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2011194/ DO - 10.1051/cocv/2011194 LA - en ID - COCV_2013__19_1_1_0 ER -
%0 Journal Article %A Bousquet, Pierre %T Continuity of solutions of a nonlinear elliptic equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1-19 %V 19 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2011194/ %R 10.1051/cocv/2011194 %G en %F COCV_2013__19_1_1_0
Bousquet, Pierre. Continuity of solutions of a nonlinear elliptic equation. ESAIM: Control, Optimisation and Calculus of Variations, Volume 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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