Gradient continuity estimates

By Frank Duzaar, Giuseppe Mingione. 2010

120 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/bcb67c952a16c5629018e8bb6340cbadc4bcf85b

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. Giuseppe Mingione
2. Tuomo Kuusi
3. Andrea Cianchi
4. Vladimir G. Maz'ya
5. Frank Duzaar
6. E. Teixeira
7. Cristiana De Filippis
8. Paolo Baroni

In Computational Theory and Mathematics

1. Giuseppe Mingione
2. Tuomo Kuusi
3. Andrea Cianchi
4. Frank Duzaar
5. Vladimir G. Maz'ya
6. E. Teixeira
7. Iwona Chlebicka
8. Cristiana De Filippis

In Mathematical Physics

1. Giuseppe Mingione
2. Tuomo Kuusi
3. Vladimir G. Maz'ya
4. Andrea Cianchi
5. Frank Duzaar
6. E. Teixeira
7. Paolo Baroni
8. Cristiana De Filippis

Citations in the corpus

• Linear Potentials in Nonlinear Potential Theory (2013, background): “The results extends also to fully nonlinear elliptic equations as F (Du) = 0 as eventually shown in [8], and upgrades to the optimal level a previous continuity criterion obtained in [11], claiming the continuity of the gradient in the case μ ∈ L(n, 1/(p − 1)).”
• Gradient estimates via non-linear potentials (2009, methodology): “worth mentioning that the Lipschitz continuity estimates and the techniques of this paper are the starting point for further developments, eventually leading to C1-regularity assertions for solutions [23]. For notation and more details we recommend the reader to look at Section 2 below. 1.1. Degener”
• Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations (2010, methodology): “gif"/> has also been shown to ensure the continuity of the gradient of solutions to p -Laplacian equations [ 18 ].”
• Regularity for quasilinear equations on degenerate singular sets (2012, background): “Theorem 1 ([3], Theorem 4 and [7], Theorem 1.”
• Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems (2012, unknown): “It has also been shown, via a different approach relying upon potential theory, to ensure the inner local boundedness of the gradient of local solutions to equations and to systems with Uhlenbeck structure [21], and also its continuity [22].”
• Nonlinear Measure Data Problems (2011, background): “4 ([39, 67, 68]).”
• A nonlinear Stein theorem (2014, background): “We remark that a preliminary gradient continuity result for solutions to (3) has been obtained in [7] for the case p ≥ 2 and under the suboptimal assumptions F ∈ L ( n, 1 p− 1 ) and ∫”
• Gradient potential estimates (2011, background): “19) also implies estimates in noninterpolation spaces such as Morrey spaces, of the type obtained in [27, 28, 29]; see also the forthcoming papers [16, 17].”