scholarly journals Weighted distribution approach to gradient estimates for quasilinear elliptic double-obstacle problems in Orlicz spaces

2021 ◽  
pp. 125928
Author(s):  
Minh-Phuong Tran ◽  
Thanh-Nhan Nguyen
Keyword(s):  
Orlicz Spaces ◽  
Obstacle Problems ◽  
Gradient Estimates ◽  
Weighted Distribution ◽  
Quasilinear Elliptic

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

scholarly journals Global Lorentz gradient estimates for quasilinear equations with measure data for the strongly singular case: 1 < p ≤ 3n−2 2n−1

2020 ◽  
pp. 2050056
Author(s):  
Le Cong Nhan ◽  
Le Xuan Truong
Keyword(s):  
Global Regularity ◽  
Gradient Estimates ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Singular Case ◽  
Regularity Estimates ◽  
Monotonicity Conditions ◽  
Vector Valued Function ◽  
Quasilinear Elliptic ◽  
Vector Valued

In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form [Formula: see text] where [Formula: see text] is a finite signed Radon measure in [Formula: see text], [Formula: see text] is a bounded domain such that its complement [Formula: see text] is uniformly [Formula: see text]-thick and [Formula: see text] is a Carathéodory vector-valued function satisfying growth and monotonicity conditions for the strongly singular case [Formula: see text]. Our result extends the earlier results [19,22] to the strongly singular case [Formula: see text] and a recent result [18] by considering rough conditions on the domain [Formula: see text] and the nonlinearity [Formula: see text].

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