作者：Mehta, VB; Ramadas, TR
摘要：Let X be an irreducible projective curve of genus g over an algebraically closed field of positive characteristic not equal 2, 3. In Part I, we prove, adapting the degeneration arguments of [N-TR], that moduli spaces of rank-two (parabolic) bundles on X are Frobenius split [M-R] for generic smooth X. (A similar result holds for X nodal. A consequence is the Verlinde formula in positive characteristic.) In Part II, we give a direct proof of the fact that the local rings of the moduli spaces are...
作者：Hofmann, S; Lewis, JL
摘要：We consider boundary value problems for the heat equation in time-varying graph domains of the form Omega = {(x(0), x, t) is an element of R x R(n-1) x R: x(0) > A(x, t)}, obtaining solvability of the Dirichlet and Neumann problems when the data lie in L(2)(partial derivative Omega). We also prove optimal regularity estimates for solutions to the Dirichlet problem when the data lie in a parabolic Sobolev space of functions having a tangential (spatial) gradient, and one half of a time derivati...
作者：Nachman, AI
摘要：We show that the coefficient gamma(x) of the elliptic equation del . (gamma del u) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary, and give a reconstruction procedure. For the equation Sigma partial derivative(i)(gamma(ij)partial derivative(j)u) = 0, two matrix-valued functions gamma(1) and gamma(2) yield the same Dirichlet-to-Neumann map if and only if there is a diffeomorphism of the domain which fixes the boundary and tra...
