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Full-Text Articles in Physical Sciences and Mathematics
Existence And Uniqueness Of Solutions For A Fractional Boundary Value Problem On A Graph, John R. Graef, Lingju Kong, Min Wang
Existence And Uniqueness Of Solutions For A Fractional Boundary Value Problem On A Graph, John R. Graef, Lingju Kong, Min Wang
Faculty Scholarship for the College of Science & Mathematics
In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.
Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman
Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. This paper establishes additional geometric regularity properties of mediatrices. We show that mediatrices have the radial linearizability property, which implies that at each point they have a geometrically defined derivative in the branching directions. Also, we study the particular case of mediatrices on spheres, by showing that they are Lipschitz simple closed curves …