Related papers: The trace problem for vector fields satisfying H\"…

By a stronger compact boundary embedding theorem in Musielak-Orlicz-Sobolev space developed in the paper, variational method is employed to deal with the nonlinear elliptic equation with the nonlinear Neumann boundary condition in the…

We obtain Liouville type theorems for degenerate elliptic equation with a drift term and a potential. The diffusion is driven by H\"ormander operators. We show that the conditions imposed on the coefficients of the operator are optimal.…

Given any elliptic system with $t$-independent coefficients in the upper-half space, we obtain representation and trace for the conormal gradient of solutions in the natural classes for the boundary value problems of Dirichlet and Neumann…

Let $K$ be a number field, which is tame and non totally real. In this article we give a numerical criterion, depending only on the ramification behavior of ramified primes in $K$, to decide whether or not the integral trace of $K$ is…

Here we define the concept of $L$-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on ${\bf{P}^n}$. In this setting we prove analogs of some classical properties. We use our…

Let $H = H_0 + P$ denote the harmonic oscillator on $\mathbb{R}^d$ perturbed by an isotropic pseudodifferential operator $P$ of order $1$ and let $U(t) = \operatorname{exp}(- it H)$. We prove a Gutzwiller-Duistermaat-Guillemin type trace…

A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten $p$-classes for p>2 is proved

We develop a sharp boundary trace theory in arbitrary bounded Lipschitz domains which, in contrast to classical results, allows "forbidden" endpoints and permits the consideration of functions exhibiting very limited regularity. This is…

We introduce a class of "Lipschitz horizontal" vector fields in homogeneous groups, for which we show equivalent descriptions, e.g. in terms of suitable derivations. We then investigate the associated Cauchy problem, providing a uniqueness…

For every symmetrically normed ideal $\mathcal{E}$ of compact operators, we give a criterion for the existence of a continuous singular trace on $\mathcal{E}$. We also give a criterion for the existence of a continuous singular trace on…

In this paper we fix $1\le p<\infty$ and consider $(\Om,d,\mu)$ be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure $\mu$ supporting a $p$-Poincar\'e inequality such that $\Om$ is a uniform…

A complete description of traces on $\mathbb{R}^{n}$ of functions from the weighted Sobolev space $W^{l}_{1}(\mathbb{R}^{n+1},\gamma)$, $l \in \mathbb{N}$, with weight $\gamma \in A^{\rm loc}_{1}(\mathbb{R}^{n+1})$ is obtained. In the case…

We establish the local Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation within the Heisenberg group. Our approach is largely inspired by the works of X. Zhong, who investigated the q-Laplacian in the same…

We consider linear second order nonvariational partial differential operators of the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where the X_{i}'s (i=0,1,2,...,q, n>q+1) are real smooth vector fields satisfying H\"ormander's…

We consider a system of ODE in a Fr\'echet space with unconditional Schauder basis. The right side of the ODE is a discontinuous function. Under certain monotonicity conditions we prove an existence theorem for the corresponding initial…

We show that vector fields $b$ whose spatial derivative $D_xb$ satisfies a Orlicz summability condition have a spatially continuous representative and are well-posed. For the case of sub-exponential summability, their flows satisfy a Lusin…

We study the scattering problem for the Schr\"odinger equation on the half-line with Robin boundary condition at the origin. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a…

Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. We study two aspects of Reeb vector fields defined by stable Hamiltonian structures on 3-manifolds: on one…

In this paper we develop a new technique to prove existence of solutions of Fokker-Planck equations on Hilbert spaces for Kolmogorov operators with non trace-class second order coefficients or equivalently with an associated stochastic…

The natural $H^1(\Omega)$ energy norm for Helmholtz problems is weighted with the wavenumber modulus $\sigma$ and induces natural weighted norms on the trace spaces $H^{\pm1/2}(\Gamma)$ by minimial extension to $\Omega\subset\mathbb R^n$.…