# Continuity of solutions of a nonlinear elliptic equation

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 1, page 1-19
- ISSN: 1292-8119

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topBousquet, Pierre. "Continuity of solutions of a nonlinear elliptic equation." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 1-19. <http://eudml.org/doc/272871>.

@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 -

## References

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