Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

By Hongjie Dong, Doyoon Kim. 2011

92 citations recorded by the source corpus.

Abstract The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ed66c4b58814fde5baa1fea5e696dab93bc2eaf5

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In Applied Mathematics

1. Hongjie Dong
2. Doyoon Kim

In Computational Theory and Mathematics

1. Hongjie Dong
2. Doyoon Kim

In Mathematical Physics

1. Hongjie Dong
2. Doyoon Kim

Citations in the corpus

• On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights (2016, methodology): “7 of [18] by using the interior and boundary Hm q estimates, i.”