Parabolic Equations with Measurable Coefficients
By Doyoon Kim, Nicolai V. Krylov. 2006
84 citations recorded by the source corpus.
We investigate the unique solvability of second order parabolic equations in non-divergence form in $W_p^{1,2}((0,T) \times \mathbb{R}^d)$, p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/be5ee00ce8e7eb1c02b811cd87d8d13fb66018e0
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
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights (2016, background): “Such coefficients are considered in [35, 36, 33, 34, 14, 15, 16] for equations defined in the whole Euclidean space or on a half space with the Lebesgue measure and no weights.”
- Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains (2011, methodology): “The method in [27] was later further developed in a series of papers [28, 22, 23, 24, 25, 29, 17, 15, 13] on Lp-estimates of second order equations with rather general discontinuous coefficients.”