TY - JOUR
T1 - Up-to boundary regularity for a singular perturbation problem of p-Laplacian type
AU - Karakhanyan, Aram L.
PY - 2006/7/15
Y1 - 2006/7/15
N2 - In this paper we are interested in establishing up-to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular/degenerate elliptic operator. Our main result states: if Ω ⊂ Rn is a C1, α domain, f ∈ C1, α ( over(Ω, -) ) for some 0 < α < 1 and uε verifies{A formula is presented} where ε > 0, βε ( t ) = frac(1, ε) β ( frac(t, ε) ) and{A formula is presented} with some positive constants B and M, then there exists a constant C > 0 independent of ε such that {norm of matrix} ∇ uε {norm of matrix}L∞ (over(Ω, -) ) {less-than or slanted equal to} C.
AB - In this paper we are interested in establishing up-to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular/degenerate elliptic operator. Our main result states: if Ω ⊂ Rn is a C1, α domain, f ∈ C1, α ( over(Ω, -) ) for some 0 < α < 1 and uε verifies{A formula is presented} where ε > 0, βε ( t ) = frac(1, ε) β ( frac(t, ε) ) and{A formula is presented} with some positive constants B and M, then there exists a constant C > 0 independent of ε such that {norm of matrix} ∇ uε {norm of matrix}L∞ (over(Ω, -) ) {less-than or slanted equal to} C.
KW - Free boundary problem
KW - Global gradient bounds
KW - Singular perturbation problem
KW - p-Laplace operator
UR - http://www.scopus.com/inward/record.url?scp=33747622596&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2005.10.014
DO - 10.1016/j.jde.2005.10.014
M3 - Article
SN - 0022-0396
VL - 226
SP - 558
EP - 571
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -