Global gradient estimates for degenerate parabolic equations in nonsmooth domains

By Mikko Parviainen. 2009

58 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/72a0ec0809817c2c49c1757accc993cc38aab533

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. Verena Bogelein
3. Sun-Sig Byun
4. Tuomo Kuusi
5. Lihe Wang
6. Frank Duzaar
7. Paolo Baroni
8. N. Phuc

In Computational Theory and Mathematics

1. Giuseppe Mingione
2. Verena Bogelein
3. Sun-Sig Byun
4. Tuomo Kuusi
5. Lihe Wang
6. Frank Duzaar
7. Paolo Baroni
8. S. Armstrong

In Mathematical Physics

1. Giuseppe Mingione
2. Tuomo Kuusi
3. Verena Bogelein
4. Sun-Sig Byun
5. Frank Duzaar
6. Lihe Wang
7. S. Armstrong
8. Paolo Baroni

Citations in the corpus

• Potential estimates and gradient boundedness for nonlinear parabolic systems (2012, background): “We remark that since the work of DiBenedetto in the eighties – see [5] for an overview– the intrinsic geometry viewpoint has proved to be unavoidable in studying parabolic equations with p-growth; see for instance [25] and [35].”
• Self-improving property of nonlinear higher order parabolic systems near the boundary (2010, background): “4) as in [36] for h, we can absorb the first term on the right-hand side into the left, because the left-hand side matches with (6.”
• Nonlinear gradient estimates for elliptic equations of general type (2012, background): “We would like to point out that a sort of improved regularity for nonlinear elliptic and parabolic equations in nonsmooth domains was investigated for the purpose of finding an optimal geometric condition on the boundary under which Poincaré’s inequality still holds true, see [16,20,21].”
• The boundary regularity of non-linear parabolic systems I (2010, background): “By an up to the initial boundary higher integrability result as for instance provided by [8,31] we infer the existence of σ1 = σ1(n,N,L/ν) > 2 such that Du ∈ Lσ1(Q0 (z0);RNn).”
• Quantitative stochastic homogenization and regularity theory of parabolic equations (2017, background): “Global versions of the Meyers estimate in the parabolic setting have been previously considered in [27],”
• Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, background): “The case 2n n+2 < p 6= 2 goes back to the work of Kinnunen and Lewis [29], and for a global version we refer to [38].”
• Global Calderón–Zygmund theory for nonlinear parabolic systems (2013, methodology): “The interior result was first established by Kinnunen & Lewis [29] and subsequently generalized in different directions, cf. [4, 11, 34].”