Abstract
We address the regularity of solutions to elliptic and parabolic equations of the form -δu + b - ∇u = 0 and ut - Δu + b - ∇u = 0 with divergence-free drifts b. We are particularly interested in the case when the drift velocity b is assumed to be at the supercritical regularity level with respect to the natural scaling of the equations. Using Harnack-type inequalities obtained in our previous works [7] and [8], we prove the uniform continuity of solutions when the drift b lies in a slightly supercritical logarithmic Morrey spaces.
Original language | English (US) |
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Pages (from-to) | 81-86 |
Number of pages | 6 |
Journal | Advances in Nonlinear Analysis |
Volume | 3 |
Issue number | 2 |
DOIs | |
State | Published - May 1 2014 |
All Science Journal Classification (ASJC) codes
- Analysis
Keywords
- Drift-diffusion equations
- Harnack inequality
- Regularity