Browsing by Subject "partial differential equations"
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On Holder continuity of weak solutions to degenerate linear elliptic partial differential equations
(2013-08-21)For degenerate elliptic partial differential equations, it is often desirable to show that a weak solution is smooth. The first and most difficult step in this process is establishing local Hölder continuity. Sufficient ... -
Pattern Formation in Bacterial Colonies with Density-Dependent Diffusion
(2017-04-07)Recent experiments have shown that patterns can emerge in bacterial colonies programmed to have a drop in diffusion when population densities (detected via a quorum sensing mechanism) are sufficiently large. We examine one ...