相关论文: Lineability and spaceability for the weak form of …

The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…

In this paper we establish some new results concerning the Cauchy-Peano problem in Banach spaces. Firstly, we prove that if a Banach space $E$ admits a fundamental biorthogonal system, then there exists a continuous vector field $f\colon…

G\'amez-Merino, Munoz-Fern\'andez and Seoane-Sep\'ulveda proved that if additivity $\mathcal A(\mathcal F)>\mathfrak c$, then $\mathcal F$ is $\mathcal A(\mathcal F)$-lineable where $\mathcal F\subseteq\mathbb R^\mathbb R$. They asked if…

In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…

A subset $A$ of a vector space $X$ is called $\alpha$-lineable whenever $A$ contains, except for the null vector, a subspace of dimension $\alpha$. If $X$ has a topology, then $A$ is $\alpha$-spaceable if such subspace can be chosen to be…

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…

The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval onto the unit square. From this fact one can easily construct of a continuous surjection from the real line…

We study functions of least gradient as well as related superminimizers and solutions of obstacle problems in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show a standard weak Harnack…

We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every…

We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Peano's or Picard's theorems). We illustrate our results with…

Recently a new approach to varying exponent $L^{p(\cdot)}$ space norms employing weak solutions to first order ordinary differential equations was initiated by the author. The duality of these ODE-determined $L^{p(\cdot)}$ spaces is…

Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend…

We consider Sobolev spaces with values in Banach spaces as they are frequently useful in applied problems. Given two Banach spaces $X\neq\{0\}$ and $Y$, each Lipschitz continuous mapping $F:X\rightarrow Y$ gives rise to a mapping $u\mapsto…

Let $f:V\times V\to F$ be a totally arbitrary bilinear form defined on a finite dimensional vector space $V$ over a a field $F$, and let $L(f)$ be the subalgebra of $\gl(V)$ of all skew-adjoint endomorphisms relative to $f$. Provided $F$ is…

The aim of this paper is to introduce new forms of the weak and Omori-Yau maximum principles for linear operators, notably for trace type operators, and show their usefulness, for instance, in the context of PDE's and in the theory of…

The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end we apply the relative energy concept provided by [3]. We consider the case of…

We propose a new guiding principle for phenomenology: special geometry in the vacuum space. New algorithmic methods which efficiently compute geometric properties of the vacuum space of N=1 supersymmetric gauge theories are described. We…

A well-known theorem of Assouad states that metric spaces satisfying the doubling property can be snowflaked and bi-Lipschitz embedded into Euclidean spaces. Due to the invariance of many geometric properties under bi-Lipschitz maps, this…

We prove an extension theorem for local solutions of the 3d incompressible Euler equations. More precisely, we show that if a smooth vector field satisfies the Euler equations in a spacetime region $\Omega\times(0,T)$, one can choose an…

Using the standard Whitney topologies on spaces of Lorentzian metrics, we show that the existence of causal incomplete geodesics is a $C^\infty$-generic feature within the class of spacetimes of a given dimension $n\geq 3$ that are stably…