Potential estimates and gradient boundedness for nonlinear parabolic systems
By Tuomo Kuusi, Giuseppe Mingione. Revista matemática iberoamericana, 2012
59 citations recorded by the source corpus.
We consider a class of parabolic systems and equations in divergence form modeled by the evolutionary p-Laplacean system ut div(jDuj p 2 Du) = V (x;t); and provide L 1 -bounds for the spatial gradient of solutions Du via non- linear potentials of the right hand side datum V. Such estimates are related to those obtained by Kilpelainen & Mal y (22) in the elliptic case.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d3686bc4e7facf17cf1857d79b00472d92cec03c
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In Applied Mathematics
- Tuomo Kuusi
- Giuseppe Mingione
- Cristiana De Filippis
- Paolo Baroni
- Frank Duzaar
- Giampiero Palatucci
- Verena Bogelein
- Sun-Sig Byun
In Computational Theory and Mathematics
- Tuomo Kuusi
- Giuseppe Mingione
- Frank Duzaar
- Paolo Baroni
- Cristiana De Filippis
- Verena Bogelein
- Sun-Sig Byun
- Jan Kristensen
In Mathematical Physics
- Tuomo Kuusi
- Giuseppe Mingione
- Paolo Baroni
- Cristiana De Filippis
- Vicentiu D. Rădulescu
- Frank Duzaar
- Giampiero Palatucci
- Patrick Winkert
Citations in the corpus
- Riesz Potentials and Nonlinear Parabolic Equations (2013, background): “2 substantially improves the ones in [23] claiming only the boundedness of the gradient under the assumption μ ∈ L(N, 1); see also [6] for a related global boundedness result in the elliptic case.”
- The Wolff gradient bound for degenerate parabolic equations (2014, background): “Exactly as for instance in [24]—but this is actually standard—it follows that aσ (·) satisfies (1.”