Local boundedness of solutions to non-local parabolic equations modeled on the fractional p-Laplacian
By Martin H. Strömqvist. Journal of Differential Equations, 2019
63 citations recorded by the source corpus.
Abstract We state and prove estimates for the local boundedness of subsolutions of non-local, possibly degenerate, parabolic integro-differential equations of the form ∂ t u ( x , t ) + P.V. ∫ R n K ( x , y , t ) | u ( x , t ) − u ( y , t ) | p − 2 ( u ( x , t ) − u ( y , t ) ) d y = 0 , ( x , t ) ∈ R n × R , where P.V. means in the principle value sense, p ∈ ( 1 , ∞ ) and the kernel obeys K ( x , y , t ) ≈ | x − y | n + p s for some s ∈ ( 0 , 1 ) , uniformly in ( x , y , t ) ∈ R n × R n × R .
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/eb66be10b6ddac540828d79c6666b11266b4a87a
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
- P. Garain
- Juha Kinnunen
- Verena Bogelein
- Frank Duzaar
- Giuseppe Mingione
- Anders Bjorn
- Tuomo Kuusi
- Mikko Parviainen
In Computational Theory and Mathematics
- P. Garain
- Juha Kinnunen
- Verena Bogelein
- Frank Duzaar
- Giuseppe Mingione
- Tuomo Kuusi
- Mikko Parviainen
- Anders Bjorn
Citations in the corpus
- On the regularity theory for mixed local and nonlocal quasilinear elliptic equations (2021, background): “Strömqvist [39] obtained a local boundedness result for weak subsolutions with p > 2.”