Interior Gradient Estimates for Nonuniformly Parabolic Equations II

We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no restrictions on the maximum eigenvalue of the coefficient matrix and we obtain interior gradient estimates for so-called false mean curvature equation

Time-Periodic Solutions of Quasilinear Parabolic Differential Equations I. Dirichlet Boundary Conditions

AbstractWe study boundary value problems for quasilinear parabolic equations when the initial condition is replaced by periodicity in the time variable. Our approach is to relate the theory of such problems to the classical theory for initial-boundary value problems. In the process, we generalize many previously known results

Securely Handling Inter-Application Connection Credentials

The utilization of application-to-application (A2A) credentials within interpretive language scripts and application code has long been a security risk. The quandaries being how to protect and secure the credentials handled in the main body of code and avoid exploitation from rogue programmers, system administrators and other users with authorized high levels of privilege. Researchers report that A2A credentials cannot be protected and that there is no way to reduce the risk of the inevitable successful attack and subsequent exploit. Therefore, research efforts to date have primarily been focused on mitigating the impact of the attack rather than finding ways to reduce the attack surface. The work contained herein successfully addresses this serious cross-cutting concern and proves that it is in fact possible to significantly reduce the risk of attack. This reduction of risk was accomplished through implementing a method of credential obfuscation which applied advice with concerns utilizing a composition filter. The filter modified messages containing the credentials as they were sent from the interpretive language script to the remote data store. The modification extracted credentials from a secure password vault and inserted them into the message being sent to the remote data store. This modification moved the handling of the credentials from the main body of code to a secure library and out of the reach of attackers with authorized high levels of privilege. The relocation of the credential handling code lines significantly reduced the attack surface and the overall risk of attack

The Dirichlet problem with Lp boundary data in domains with Dini continuous normal

In a series of articles [1-4, 6-8, 15, 16, 22-26], Mikhailov, Chabrowski, and others have used energy inequality methods to study the Dirichlet problem with Lp boundary ..