The equivalence relation of concordance on the set of links of circles in 3-space arises naturally in attempts to resolve singularities of immersed 2-spheres in a 4-dimensional manifold. In fact, certain unsolved link concordance problems are exactly the obstructions to successfully performing surgery on 4-manifolds as the higher-dimensional theory predicts.

In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.

This memoir considers the Dirichlet problem for parabolic operators in a half space with singular drift terms. Chapter I begins the study of a parabolic PDE modelled on the pullback of the heat equation in certain time varying domains considered by Lewis-Murray and Hofmann-Lewis. Chapter II obtains mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the $L DEGREESq(R DEGREESn)$ Dirichlet problem for these PDEs has a solution when $q$ is large enough. Chapter III proves an analogue of a theorem of Fefferman, Kenig, and Pipher for...

Let $mathcal S$ be a second order smoothness in the $mathbb DEGREESn$ setting. We can assume without loss of generality that the dimension $n$ has been adjusted as necessary so as to insure that $mathcal S$ is also non-degenerate. This title describes how $mathcal S$ must fit into one of three mutually exclusive cases, and in each of these cases the authors characterize, by a simple intrinsic condition, the second order smoothnesses $mathcal S$ whose canonical Sobolev projection $P_$ is of weak type $(1,1)$ in the $mathbb DEGR

The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz subdomains of Riemannian manifolds. In the first part it develops a theory for Cauchy type operators on Lipschitz submanifolds of codimension one (focused on boundedness properties and jump relations). The solution is represented in the form of layer potentials and optimal nontangential maximal function estimates are established. This analysis is carried out under smoothness assumptions (for the coefficients of the operator, metric tensor and the underlying domain)...

The Second Chinburg Conjecture relates the Galois module structure of rings of integers in number fields to the values of the Artin root number on the symplectic representations of the Galois group. This book establishes the Second Chinburg Conjecture for various quaternion fields.

This book is intended for researchers and graduate students in commutative algebra, algebraic topology and invariant theory.

This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. The authors outline, analyze and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally.

This book is intended for graduate students and researchers interested in the mathematical physics and PDE.

This book is intended for graduate students and research mathematicians working in algebraic geometry.