Remarks on Hölder continuity for solutions of the p-Laplace evolution equations

AbstractWe study the interior Hölder regularity problem for the gradient of solutions of the p-Laplace evolution equations with the external forces. Misawa gave some conditions for the Hölder continuity of the gradient of solutions. We show Hölder estimates of the solutions with weaker condition as for Misawa

GRADIENT ESTIMATES FOR MEAN CURVATURE FLOW WITH NEUMANN BOUNDARY CONDITIONS

We study the mean curvature ow of graphs both with Neumann boundary conditions and transport terms. We derive boundary gradient estimates for the mean curvature ow. As an application, the existence of the mean curvature ow of graphs is presented. A key argument is a boundary monotonicity formula of a Huisken type derived using re ected backward heat kernels. Furthermore, we provide regularity conditions for the transport terms

Convergence of the Allen-Cahn equation with Neumann boundary conditions

We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.Comment: 26 pages, 1 figur

Location of phosphorylation site and DNA-binding site of a positive regulator, OmpR, involved in activation of the osmoregulatory genes of Escherichia coli

AbstractThe OmpR protein of Escherichia coli is a positive regulator involved in activation of the ompF and ompC genes which encode the major outer membrane proteins OmpF and OmpC, respectively. By employing recombinant DNA techniques, we isolated the N- and C-terminal halves of the OmpR molecule. From the results of biochemical analyses of these fragments, it was concluded that the N-terminal portion contains a site involved in phosphorylation by an OmpR-specific protein kinase EnvZ, whereas the C-terminal part possesses a DNA-binding site for the ompC and ompF promoters