# Weighted Global Regularity Estimates for Elliptic Problems with Robin Boundary Conditions in Lipschitz Domains

@article{Yang2020WeightedGR,
title={Weighted Global Regularity Estimates for Elliptic Problems with Robin Boundary Conditions in Lipschitz Domains},
author={Sibei Yang and Dachun Yang and Wen Yuan},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Published 17 March 2020
• Mathematics
• arXiv: Analysis of PDEs
2 Citations

### Stability Results for the Robin-Laplacian on Nonsmooth Domains

• Mathematics
SIAM Journal on Mathematical Analysis
• 2022
. We formulate a generalization of the Laplace equation under Robin boundary conditions on a large class of possibly nonsmooth domains by dealing with the trace term appearing in the variational

## References

SHOWING 1-10 OF 80 REFERENCES

### Gradient Weighted Norm Inequalities for Linear Elliptic Equations with Discontinuous Coefficients

• Mathematics
Applied Mathematics & Optimization
• 2018
Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence form over a Lipschitz

### Homogenization of Elliptic Problems with Neumann Boundary Conditions in Non-smooth Domains

AbstractWe consider a family of second-order elliptic operators {Lε} in divergence form with rapidly oscillating and periodic coefficients in Lipschitz and convex domains in ℝn. We are able to show

### The mixed problem in Lipschitz domains with general decompositions of the boundary

• Mathematics
• 2012
This paper continues the study of the mixed problem for the Laplacian. We consider a bounded Lipschitz domain $\Omega\subset \reals^n$, $n\geq2$, with boundary that is decomposed as

### The Mixed Problem for the Laplacian in Lipschitz Domains

• Mathematics
• 2013
We consider the mixed boundary value problem, or Zaremba’s problem, for the Laplacian in a bounded Lipschitz domain Ω in Rn, n ≥ 2. We decompose the boundary $\partial \Omega= D\cup N$ with D and N

### Coercive energy estimates for differential forms in semi-convex domains

• Mathematics
• 2010
In this paper, we prove a $H^1$-coercive estimate for differential forms of arbitrary degrees in semi-convex domains of the Euclidean space. The key result is an integral identity involving a

• Mathematics
• 2017
Consider the nonlinear parabolic equation in the form \begin{aligned} u_t-\mathrm{div}{\mathbf {a}}(D u,x,t)=\mathrm{div}\,(|F|^{p-2}F) \quad \text {in} \quad \Omega \times (0,T), ### On necessary and sufficient conditions for L^p-estimates of Riesz transforms associated to elliptic operators on \RR^n and related estimates This article focuses on L^p estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz ### UniformW^{1,p}$$estimates for an elliptic operator with Robin boundary condition in a$$\mathcal {C}^1 domain

• Mathematics
Calculus of Variations and Partial Differential Equations
• 2020
We consider the Robin boundary value problem $\mathrm{div} (A \nabla u) = \mathrm{div} \mathbf{f}+F$ in $\Omega$, $\mathcal{C}^1$ domain, with \$(A \nabla u - \mathbf{f})\cdot \mathbf{n} + \alpha u =