An improved convexity maximum principle and some applications

Fractional convexity maximum principle∗

We construct an anisotropic, degenerate, fractional operator that nevertheless satisfies a strong form of the maximum principle. By applying such an operator to the concavity function associated to the solution of an equation involving the usual fractional Laplacian, we obtain a fractional form of the celebrated convexity maximum principle devised by Korevaar in the 80’s. Some applications are ...

Maximum Principle for Spdes and Its Applications

The maximum principle for SPDEs is established in multidimensional C domains. An application is given to proving the Hölder continuity up to the boundary of solutions of one-dimensional SPDEs. The maximum principle is one of the most powerful tools in the theory of second-order elliptic and parabolic partial differential equations. However, until now it did not play any significant role in the ...

Applications of convexity in some identification problems

The Contraction Mapping Principle and Some Applications

These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in the theories of differential and integral equations and variational inequalities are given. Also discussed are Hilbert’s projective metric and iterated function systems

Some improved results on the convexity of fuzzy nets

In this paper, we give some improved results on the θ-convex hull of fuzzy net in the literature. 2010 AMS Classification: 03E72, 08A72