Very weak solutions of parabolic systems ofp-Laplacian type

By Juha Kinnunen, John L. Lewis. 2002

96 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9cfb643c8ff002a1bdb677f5c386e0148295bf23

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. Paolo Baroni
3. Verena Bogelein
4. Frank Duzaar
5. Tuomo Kuusi
6. Lars Diening
7. P. Hasto
8. Sun-Sig Byun

In Computational Theory and Mathematics

1. Giuseppe Mingione
2. Paolo Baroni
3. Verena Bogelein
4. Frank Duzaar
5. Tuomo Kuusi
6. P. Hasto
7. Lars Diening
8. Jihoon Ok

Citations in the corpus

• Riesz Potentials and Nonlinear Parabolic Equations (2013, background): “Du(x0,t0)| ≤ λ. Both (1.15) and (1.16) are basic results of DiBenedetto [9] while we just remark that intrinsic geometries are nowadays a basic and common tool to treat degenerate parabolic equations [1, 19, 20]. Thepreviousconsiderations, togetherwith (1.15)-(1.16), areactuallythe starting point fo”
• Hölder estimates for parabolic p(x, t)-Laplacian systems (2012, methodology): “For the case of parabolic systems satisfying a standard p-growth we mention the work of Kinunnen and Lewis [23] (for the higher order analogue see [7]), and the related results [8,24] for very weak solutions of systems of this type.”
• SOLENOIDAL LIPSCHITZ TRUNCATION FOR PARABOLIC PDEs (2012, background): “Further results about parabolic Lipschitz truncation are due to Kinnunen-Lewis[14].”
• Existence of weak solutions for unsteady motions of generalized Newtonian fluids (2010, methodology): “Similar results have been proved in [24].”
• Very weak solutions of nonlinear subelliptic equations (2005, result): “Recently, a similar theorem on very weak solutions for parabolic equations (in case X = r) was proved by J. Lewis and J. Kinnunen [18], [ 19 ].”
• Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, methodology): “This can be overcome by a variety of different techniques such as the nonlinear Hodge decomposition from [28] or a Whitney type construction of suitable test functions from [33], [30].”
• Gradient estimates for a class of parabolic systems (2007, background): “There has recently been a great deal of work concerning the integrability properties of weak and \very weak" solutions to systems similar to (1), see [16, 17 , 18].”
• Lorentz estimates for degenerate and singular evolutionary systems (2013, background): “In particular we consider here the elliptic system div [ c(x)|Du|p−2Du ] = div [ |G|p−2G ] in Ω, (1.6) where Ω is again a bounded connected open set of Rn and u maps Ω into RN ; we can consider here the full range p > 1, since in the elliptic case the restriction in (1.1) is not anymore necessary.”
• Harmonic type approximation lemmas (2009, background): “available but in a non-homogeneous form, see [52,53,31], which does not fit in the standard partial regularity proofs based on such a tool.”
• HIGHER INTEGRABILITY FOR WEAK SOLUTIONS OF HIGHER ORDER DEGENERATE PARABOLIC SYSTEMS (2008, methodology): “This method turned out to be fruitful also when considering systems of more general structure and it was used in [13, 14] by Kinnunen and Lewis to show higher integrability for second order parabolic systems in the case p 6= 2.”