TY - JOUR
T1 - Weighted variable exponent Sobolev estimates for elliptic equations with non-standard growth and measure data
AU - Bui, The Anh
AU - Duong, Xuan Thinh
PY - 2018/8/1
Y1 - 2018/8/1
N2 - Consider the following nonlinear elliptic equation of p(x)-Laplacian type with nonstandard growth {diva(Du,x)=μ in Ω, u=0 on ∂Ω, where Ω is a Reifenberg domain in Rn, μ is a Radon measure defined on Ω with finite total mass and the nonlinearity a: Rn× Rn→ Rn is modeled upon the p(·) -Laplacian. We prove the estimates on weighted variable exponent Lebesgue spaces for gradients of solutions to this equation in terms of Muckenhoupt–Wheeden type estimates. As a consequence, we obtain some new results such as the weighted Lq- Lr regularity (with constants q < r) and estimates on Morrey spaces for gradients of the solutions to this non-linear equation.
AB - Consider the following nonlinear elliptic equation of p(x)-Laplacian type with nonstandard growth {diva(Du,x)=μ in Ω, u=0 on ∂Ω, where Ω is a Reifenberg domain in Rn, μ is a Radon measure defined on Ω with finite total mass and the nonlinearity a: Rn× Rn→ Rn is modeled upon the p(·) -Laplacian. We prove the estimates on weighted variable exponent Lebesgue spaces for gradients of solutions to this equation in terms of Muckenhoupt–Wheeden type estimates. As a consequence, we obtain some new results such as the weighted Lq- Lr regularity (with constants q < r) and estimates on Morrey spaces for gradients of the solutions to this non-linear equation.
KW - Measure data
KW - Nonlinear p(x)-Laplacian type equation
KW - Reifenberg domain
KW - Weighted generalized Lebesgue spaces
UR - http://www.scopus.com/inward/record.url?scp=85048261187&partnerID=8YFLogxK
UR - http://purl.org/au-research/grants/arc/DP160100153
U2 - 10.1007/s00030-018-0520-z
DO - 10.1007/s00030-018-0520-z
M3 - Article
AN - SCOPUS:85048261187
SN - 1021-9722
VL - 25
SP - 1
EP - 37
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 4
M1 - 28
ER -