Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients

By Yanyan Li, Michael S. Vogelius. 2000

350 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a74c823c0f290c2c68edd636145659066d8bf782

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Hengguang Li
2. Haigang Li
3. Hui-Chun Zhang
4. Victor Nistor
5. Xiping Zhu
6. J. Bao
7. A. Mazzucato
8. Hongjie Dong

In Computational Theory and Mathematics

1. Haigang Li
2. Hengguang Li
3. J. Bao
4. Yanyan Li
5. A. Mazzucato
6. Habib M. Ammari
7. Victor Nistor
8. Hyundae Lee

In Mathematical Physics

1. Haigang Li
2. J. Bao
3. Yanyan Li
4. Hengguang Li
5. Habib M. Ammari
6. Victor Nistor
7. Hongjie Dong
8. Hyundae Lee

Citations in the corpus

• Electrical impedance tomography (2002, background): “However, it is easy to see that there exist many functions γ (x, ω)which are not even continuous, and they still give φ ∈ W 1,∞( ) (see [20, 112] for two such examples).”
• Spectral Analysis of the Neumann–Poincaré Operator and Characterization of the Stress Concentration in Anti-Plane Elasticity (2012, background): “If k stays away from 0 and ∞, that is, c1 < k < c2 for some positive constants c1 and c2, then |∇u| is bounded regardless of ε as was proved in [10,18,19].”
• Gradient estimates for solutions of the Lam\'e system with partially infinite coefficients in dimensions greater than two (2016, background): “See Bonnetier and Vogelius [16] and Li and Vogelius [33] for corresponding results on divergence form elliptic equations.”
• Yau's gradient estimates on Alexandrov spaces (2010, methodology): “In the previous version of this paper, by using some complica ted pointwise C1-estimate of elliptic equation (see, for example, [7, 27]), we can actually show that |∇u| is continuous at almost all inΩ.”
• Optimal gradient estimates of solutions to the insulated conductivity problem in dimension greater than two (2021, positive): “Later, Bonnetier and Vogelius [12] proved that when ε = 0, |∇uk| is bounded for a fixed k and circular inclusions D1 and D2 in dimension n = 2.”
• Gradient estimates for solutions to the conductivity problem (2005, methodology): “Li and Vogelius derived in [8] a uniform upper bound on the gradient of u that is independent of the distance between the inclusions B1 and B2.”
• Optimal regularity for elliptic transmission problems including C1 interfaces (2006, result): “Furthermore, it is somewhat similar to the results of [41], where piecewise Hölder continuity of the first order derivatives is proved under slightly stronger assumptions on the data.”
• Estimates for elliptic systems from composite material (2003, neutral): “1 for scalar equations was established in [10] for slightly more restrictive α′: 0 < α′ ≤ μ and α′ < α n(α+1) .”
• ANALYSIS OF THE FINITE ELEMENT METHOD FOR TRANSMISSION/MIXED BOUNDARY VALUE PROBLEMS ON GENERAL POLYGONAL DOMAINS ∗ (2010, background): “Let us nevertheless mention here the papers of Kellogg [40], Kellogg and Aziz [6], Mitrea, Mitrea, and Shi [58], Li and Nirenberg [50], Li and Vogelius [51], Roitberg and Sheftel [68] [69], Schechter [72], and others.”
• Optimal Estimates for the Conductivity Problem by Green’s Function Method (2016, methodology): “Construction of a Green’s function In this section, we construct a Green’s function of the operator Lε;r1,r2 by adapting an idea in [21].”