Higher integrability for parabolic systems of p-Laplacian type

By Juha Kinnunen, John L. Lewis. 2000

211 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a46e2168be29886444fbb29c05f5fc90f056fb38

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Self-improving property of nonlinear higher order parabolic systems near the boundary (2010, methodology): “Higher integrability for more general parabolic systems with non-linear growth conditions remained open for some time: The first positive result for degenerate and singular second order parabolic p-growth systems was obtained by Kinnunen and Lewis [26].”
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.”
Global gradient estimates for degenerate parabolic equations in nonsmooth domains (2009, background): “4 in Kinnunen and Lewis [19].”
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.”
Gradient estimates for a class of parabolic systems (2007, methodology): “We start with the higher integrability result of Kinnunen & Lewis [16], which is essential here to treat the case where the coefficient function a(z) is not continuous.”
Second order parabolic systems, optimal regularity, and singular sets of solutions (2005, methodology): “For such systems higher integrability of solutions has been recently proved by Kinnu Lewis [24], and later refined by Misawa [32], but their proof does not yield a Reverse–Hölder inequality sin scaling for parabolic systems of the type in (1.”
Very weak solutions of parabolic systems ofp-Laplacian type (2002, unknown): “by p-~ and use Lemma 4.19 (with t)=~ and s=g), as well as Lemma 4.25 (with t)=6~ and s=36~), in place of Lemma 3.2, (3.11) and (3.24) in [ KLe ].”
Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, background): “Caccioppoli inequality It is a well know fact that the first step towards a higher integrability result for solutions to elliptic and parabolic systems is a suitable Caccioppoli-type inequality (see for example [29], [30], [7], [8]).”
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.”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “2 to the case of parabolic systems with p-growth has been achieved by Kinnunen & Lewis in [198]; for the case p = 2 see [163].”
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”
Global Calderón–Zygmund theory for nonlinear parabolic systems (2013, methodology): “The interior result was first established by Kinnunen and Lewis [29] and subsequently generalized in different directions, cf.”