Continuity of solutions of a nonlinear elliptic equation

@article{Bousquet2013,
abstract = {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 ais radial: $a(\xi )=\{l(|\xi |)\}\{|\xi |\} \xi $ a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasingl:ℝ+ → ℝ+.},
author = {Bousquet, Pierre},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {nonlinear elliptic equations; continuity of solutions; lower bounded slope condition; Lavrentiev phenomenon},
language = {eng},
number = {1},
pages = {1-19},
publisher = {EDP-Sciences},
title = {Continuity of solutions of a nonlinear elliptic equation},
url = {http://eudml.org/doc/272871},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Bousquet, Pierre
TI - Continuity of solutions of a nonlinear elliptic equation
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 1
SP - 1
EP - 19
AB - 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 ais radial: $a(\xi )={l(|\xi |)}{|\xi |} \xi $ a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasingl:ℝ+ → ℝ+.
LA - eng
KW - nonlinear elliptic equations; continuity of solutions; lower bounded slope condition; Lavrentiev phenomenon
UR - http://eudml.org/doc/272871
ER -