LAGRANGIAN FLOWS FOR VECTOR FIELDS WITH GRADIENT GIVEN BY A SINGULAR INTEGRAL
2013 ◽
Vol 10
(02)
◽
pp. 235-282
◽
Keyword(s):
We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an L1 function. Such estimates allow to prove existence, uniqueness, quantitative stability and compactness for the flow, going beyond the BV theory. We illustrate the related well-posedness theory of Lagrangian solutions to the continuity and transport equations.
1991 ◽
Vol 11
(3)
◽
pp. 443-454
◽
2007 ◽
Vol 463
(2087)
◽
pp. 2929-2944
◽
1963 ◽
Vol 6
(1)
◽
pp. 43-54
1991 ◽
Vol 110
(1)
◽
pp. 207-224
◽
Keyword(s):