Related papers: The dbar-Neumann problem in the Sobolev topology
This paper is a natural continuation of paper "On rectifiable spaces and its algebraical equivalents, topological algebraic systems and Mal'cev algebras" published in arxiv:1309.4572. Thus we justify the need to present the entire material…
We extend some classical inequalities between the Dirichlet and Neumann eigenvalues of the Laplacian to the context of mixed Steklov--Dirichlet and Steklov--Neumann eigenvalue problems. The latter one is also known as the sloshing problem,…
The b -> ssdbar and b -> ddsbar decays are highly suppressed in the SM, and are thus good probes of new physics (NP) effects. We discuss in detail the structure of the relevant SM effective Hamiltonian pointing out the presence of nonlocal…
We consider parabolic equations with operators $\mathcal{L}=\partial_{t}+a^{ij}D_{ij}+b^{i}D_{i}-c$ with $a$ being almost in VMO, $b$ in a Morrey class containing $ L_{d+2}$ and $c $ in a Morrey class containing $L_{(d+2)/2}$. We prove the…
A comment to the paper by S. Chen, H. B\"uttner, and J. Voit, [Phys. Rev. Lett. {\bf 87}, 087205 (2001)].
We consider the Gel'fand inverse problem and continue studies of [Mandache,2001]. We show that the Mandache-type instability remains valid even in the case of Dirichlet-to-Neumann map given on the energy intervals. These instability results…
The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.
The symmetry breaking is obtained for Neumann problems driven by $p$-Laplacian in certain non-convex cones. These problems are generated by the Hardy--Sobolev inequalities. In the case of the Sobolev inequality for the ordinary Laplacian…
We consider the space $\mathcal{D}'^r_L(M;E)$ of distributional sections of the smooth complex vector bundle $E\rightarrow M$ whose Sobolev wave front set of order $r\in\mathbb{R}$ lies in the closed conic subset $L$ of $T^*M\backslash0$.…
This article concerns the time growth of Sobolev norms of classical solutions to the 3D quasi-linear wave equations with the null condition.
We introduce modified energies that are suitable to get upper bounds on the high Sobolev norms for solutions to the $1$D periodic NLS. Our strategy is rather flexible and allows us to get a new and simpler proof of the bounds obtained by…
A construction of blowing up solutions to the modified Novikov-Veselov equation is proposed. It is based on the Moutard transformation of two-dimensional Dirac operators and its geometrical interpretation via surface geometry. An explicit…
An updated version with a few corrections.
We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in divergence form in $\bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.
We improve the concept of our previous paper "Dirac type tensor equations with nonabelian gauge symmetries on pseudo-Riemannian space" and present a new compact formula for the tensor $B_\mu$.
We investigate Sobolev and Hardy inequalities, specifically weighted Minerbe's type estimates, in noncompact complete connected Riemannian manifolds whose geometry is described by an isoperimetric profile. In particular, we assume that the…
The purpose of this paper is twofold. We first prove a weighted Sobolev inequality and part of a weighted Morrey's inequality, where the weights are a power of the mean curvature of the level sets of the function appearing in the…
Let (M,g) be a compact Riemannien Manifold of dimension n > 2, x_0 in M a fix and singular point and s in (0,2). We let 2*(s) = 2(n-s)/(n-2) be the critical Hardy-Sobolev exponent. we investigate the existence of positive distributional…
We establish improved CR Sobolev inequalities on CR sphere under the vanishing of higher order moments of the volume element. As a direct application, we give a simpler proof of the existence and the classification of minimizers of the CR…
This manuscripts corrects some minor error in the paper, Mod. Phys. Lett. A 6 1893 (1991)