Logan F. Stokols
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View article: The De Giorgi method : applications to degenerate PDE
The De Giorgi method : applications to degenerate PDE Open
The De Giorgi method was developed in 1957 for showing continuity of non-linear elliptic problems. In this work we will apply generalizations of that method to a variety of degenerate problems. Such problems include first-order equations w…
View article: L^2-type contraction of viscous shocks for large family of scalar conservation laws
L^2-type contraction of viscous shocks for large family of scalar conservation laws Open
In this paper we study small shocks of 1D scalar viscous conservation laws with uniformly convex flux and nonlinear dissipation. We show that such shocks are L2 stable independent of the strength of the dissipation, even with large perturb…
View article: Hölder Continuity for a Family of Nonlocal Hypoelliptic Kinetic Equations
Hölder Continuity for a Family of Nonlocal Hypoelliptic Kinetic Equations Open
In this work, Holder continuity is obtained for solutions to the nonlocal kinetic Fokker-Planck Equation, and to a family of related equations with general integro-differential operators. These equations can be seen as a generalization of …
View article: Holder Continuity for a Family of Nonlocal Hypoelliptic Kinetic\n Equations
Holder Continuity for a Family of Nonlocal Hypoelliptic Kinetic\n Equations Open
In this work, Holder continuity is obtained for solutions to the nonlocal\nkinetic Fokker-Planck Equation, and to a family of related equations with\ngeneral integro-differential operators. These equations can be seen as a\ngeneralization …
View article: De Giorgi Techniques Applied to Hamilton-Jacobi Equations with Unbounded Right-Hand Side
De Giorgi Techniques Applied to Hamilton-Jacobi Equations with Unbounded Right-Hand Side Open
In this article we obtain Holder estimates for solutions to second-order Hamilton-Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estimates are uniform with respect to the smallness of the diffus…
View article: On structural decompositions of finite frames
On structural decompositions of finite frames Open
View article: On structural decompositions of finite frames
On structural decompositions of finite frames Open