Related papers: Sobolev sheaves on the plane

We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the $L^2$-based Sobolev spaces. We introduce appropriate time weighted spaces to derive…

In this paper, we extend the fractional Sobolev spaces with variable exponents $W^{s,p(x,y)}$ to include the general fractional case $W^{K,p(x,y)}$, where $p$ is a variable exponent, $s\in (0,1)$ and $K$ is a suitable kernel. We are…

A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension $m$ in $\mathbb{R}^n$ with the space of flat $m$-cochains, that is, the dual space of flat chains of dimension $m$ in $\mathbb{R}^n$.…

Let $k$ be a non-archimedean complete valued field and let X be a smooth Berkovich analytic $k$-curve. Let $F$ be a finite locally constant \'{e}tale sheaf on $k$ whose torsion is prime to the residue characteristic. We denote by $|X|$ the…

In this paper, we investigate the order algebraic structure in the category of sheaves on a given locale $X$. Since every localic topos has a generating set formed by its subterminal objects, we define a "point" of a partially ordered sheaf…

Let k be a an algebraically closed field of arbitrary characteristic, and we let h be the usual Weil height for the n-dimensional affine space corresponding to the function field k(t) (extended to its algebraic closure). We prove that for…

We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $D$. We…

We establish the existence of a solution to the Navier-Stokes equations on a moving domain with surface tension in an optimal Sobolev space for the case of two space dimension. No compatibility conditions are required to guarantee the…

We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with 1<p<\infty, and connect them to the Sobolev theory in R^n. In…

We prove that on separated algebraic surfaces every coherent sheaf is a quotient of a locally free sheaf. This class contains many schemes that are neither normal, reduced, quasiprojective or embeddable into toric varieties. Our methods…

In this paper, KdV-type equations with time- and space-dependent coefficients are considered. Assuming that the dispersion coefficient in front of $u_{xxx}$ is positive and uniformly bounded away from the origin and that a primitive…

We show that there exists a quantum compact metric space which underlies the setting of each Sobolev algebra associated to a subelliptic Laplacian $\Delta=-(X_1^2+\cdots+X_m^2)$ on a compact connected Lie group $G$ if $p$ is large enough,…

We prove local and global invertibility of Sobolev solutions of certain differential inclusions which prevent the differential matrix from having negative eigenvalues. Our results are new even for quasiregular mappings in two dimensions.

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…

We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morphism. Using this notion of morphism, we obtain (higher)…

In this paper we study the embedding properties for the weighted Sobolev space $H^1_V(\mathbb{R}^N)$ into the Lebesgue weighted space $L^\tau_W(\mathbb{R}^N)$. Here $V$ and $W$ are diverging weight functions. The different behaviour of $V$…

The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients…

The moduli stack of representations of a quiver, or coherent sheaves on a proper curve, carries two structures on its cohomology: a Hall algebra and braided vertex coalgebra. We show that they are compatible, by developing a formulation of…

In general, if M is a moduli space of stable sheaves on X, there is a unique alpha in the Brauer group of M such that a pi_M^* alpha^{-1}-twisted universal sheaf exists on X times M. In this paper we study the situation when X and M are K3…

Let Z be a zero-dimensional subscheme of the projective plane consisting of the union of r>5 double points, I its defining ideal sheaf. It is known that I has the expected cohomology when the points are distinct and in general position…