Related papers: A note on non lower semicontinuous perimeter funct…
We characterize meromorphic function fields closed by partial derivatives in n variables.
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…
We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension,…
We introduce a notion of connected perimeter for planar sets defined as the lower semi-continuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is…
In this article we study eigenvalues and minimizers of a fractional non-standard growth problem. We prove several properties on this quantities and their corresponding eigenfunctions.
We consider two relations on a $\cap$-semigroup of partial functions of a given set: the inclusion of domains and the semiadjacencity (i.e., the inclusion of the image of the first function into the domain of the second), which…
This paper is devoted to establish sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extend some results for entire functions to meromorphic functions. Actually, we shall mainly…
Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. This has led to the introduction of numerous weaker continuity…
It is shown that max-preserving maps (or join-morphisms) on the positive orthant in Euclidean $n$-space endowed with the component-wise partial order give rise to a semiring. This semiring admits a closure operation for maps that generate…
We give an overview of some applications of a general variational principle.
We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
The aim of the present paper is essentially to prove that if $\Phi$ and $\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\Psi$ is also continuous and coercive, then then following…
A spectral minimal partition of a manifold is its decomposition into disjoint open sets that minimizes a spectral energy functional. It is known that bipartite spectral minimal partitions coincide with nodal partitions of Courant-sharp…
In this paper we discuss the existence and regularity of solutions of strongly indefinite systems involving fractional elliptic operators on a smooth bounded domain $\Omega$ in $\R^n$.
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
The finite basis property is often connected with the finite rank property, which it entails. Many examples have been produced of finite rank varieties which are not finitely based. In this note, we establish a result on nilpotent…
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ is continuous. Here for bounded geometry we mean that $M$ have $Ricci$ curvature bounded below…