Cordes-Nirenberg type estimates for nonlocal parabolic equations

In this paper, we obtain Cordes-Nirenberg type estimates for nonlocal parabolic equations on the more flexible solution space L^{\iy}_T(L^1_{\om}) than the classical solution space \rB(\BR^n_T) consisting of all bounded functions on \BR^n_T.Comment: Recently our result was revised on more general solution space than the previous versio

Examples of Matrix Factorizations from SYZ

We find matrix factorization corresponding to an anti-diagonal in ${\mathbb C}P^1 \times {\mathbb C}P^1$, and circle fibers in weighted projective lines using the idea of Chan and Leung of Strominger-Yau-Zaslow transformations. For the tear drop orbifolds, we apply this idea to find matrix factorizations for two types of potential, the usual Hori-Vafa potential or the bulk deformed (orbi)-potential. We also show that the direct sum of anti-diagonal with its shift, is equivalent to the direct sum of central torus fibers with holonomy $(1,-1)$ and $(-1,1)$ in the Fukaya category of ${\mathbb C}P^1 \times {\mathbb C}P^1$, which was predicted by Kapustin and Li from B-model calculations