Related papers: The univalent Bloch-Landau constant, harmonic symm…
The Heilbronn triangle problem asks for the placement of $n$ points in a unit square that maximizes the smallest area of a triangle formed by any three of those points. In $1972$, Schmidt considered a natural generalization of this problem.…
We show the existence of solution in the maximal $L_p-L_q$ regularity framework to a class of symmetric parabolic problems on a uniformly $C^2$ domain in ${\mathcal R}$. Our approach consist in showing ${\mathcal R}$ - boundedness of…
A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…
We solve by Chebyshev spectral collocation some genuinely nonlinear Liouville-Bratu-Gelfand type, 1D and a 2D boundary value problems. The problems are formulated on the square domain $[-1, 1]\times[-1, 1]$ and the boundary condition…
A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms…
We prove a sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in a class of weighted Poincar\'e inequalities. The key point is the study of an optimal weighted Wirtinger inequality.
We consider the family of non-local and non-convex functionals proposed and investigated by J. Bourgain, H. Brezis and H.-M. Nguyen in a series of papers of the last decade. It was known that this family of functionals Gamma-converges to a…
This paper deals with a priori pointwise error estimates for the finite element solution of boundary value problems with Neumann boundary conditions in polygonal domains. Due to the corners of the domain, the convergence rate of the…
We prove \emph{uniform solvability estimates} for certain families of elliptic problems posed in a bounded family of domains (for example, a sequence that converges to another domain). We provide uniform estimates both in weighted and in…
The object of the paper is to find complete systems of inequalities relating the perimeter $P$, the area $|\cdot|$ and the Cheeger constant $h$ of planar sets. To do so, we study the so called Blaschke--Santal\'o diagram of the triplet…
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
The Hayman-Wu theorem states that the preimage of a line or circle L under a conformal mapping from the unit disc to a simply-connected domain U has total Euclidean length bounded by an absolute constant. The best possible constant is known…
A Lorentz and gauge symmetry preserving regularization method has been proposed recently in 4 dimension based on Euclidean momentum cutoff. It is shown that the triangle anomaly can be calculated unambiguously with this new improved cutoff.…
We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain with the first-kind boundary integral equation arising from the latter when constant…
We study regularity of solutions $u$ to $\overline\partial u=f$ on a relatively compact $C^2$ domain $D$ in a complex manifold of dimension $n$, where $f$ is a $(0,q)$ form. Assume that there are either $(q+1)$ negative or $(n-q)$ positive…
Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic…
Continuing our previous work (Cohn, Lam, Lu, Yang, Nonlinear Analysis (2011), doi: 10.1016 /j.na.2011.09.053), we obtain a class of Trudinger-Moser inequalities on the entire Heisenberg group, which indicate what the best constants are. All…
We investigate both the instantaneous loss and the persistence of high regularity for the one-dimensional logarithmic Schr{\"o}dinger equation in symmetric domains under various boundary conditions. We show that for a broad class of odd…
In this paper we prove a $C^{1,\alpha}$ regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase Alt-Caffarelli-Friedman functionals for an energy with variable coefficients. As…
We consider a problem relating to magnetic confinement devices known as stellarators. Plasma is confined by magnetic fields generated by current-carrying coils, and here we investigate how closely to the plasma they need to be positioned.…