相关论文: A Picard-Lindel\"of theorem for smooth PDE

We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian-Sobolev space). Our result covers first-order…

We consider Calder{\'o}n's problem on a class of Sobolev extension domains containing non-Lipschitz and fractal shapes. We generalize the notion of Poincar{\'e}-Steklov (Dirichlet-to-Neumann) operator for the conductivity problem on such…

We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…

We consider a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with coinvariant derivatives and a right-end boundary condition. Such problems arise naturally in the study of properties of the value functional in…

We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of…

We show that the Dirichlet problem at infinity is unsolvable for the p-Laplace equation for any nonconstant continuous boundary data, for certain range of p>n, on an n-dimensional Cartan-Hadamard manifold constructed from a complete…

Let X_1 ,..., X_n be a collection of binary valued random variables and let f : {0,1}^n -> R be a Lipschitz function. Under a negative dependence hypothesis known as the {\em strong Rayleigh} condition, we show that f - E f satisfies a…

The Landau equations give a physically useful criterion for how singularities arise in Feynman amplitudes. Furthermore, they are fundamental to the uses of perturbative QCD, by determining the important regions of momentum space in…

In this note, at first we prove that the existence of best proximity points for cyclic relatively nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic relatively nonexpansive mappings in the setting of…

The paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool one employs the directional limiting coderivative which, together with the graphical…

We introduce two new classes of single-valued contractions of polynomial type defined on a metric space. For the first one, called the class of polynomial contractions, we establish two fixed point theorems. Namely, we first consider the…

We develop the theory of Riemann-Hilbert problems necessary for the results in part one of this series of papers. In particular, we obtain solutions for a family of non-linear Riemann-Hilbert problems through classical contraction…

We study the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional Banach spaces, using a kind of Palais-Smale condition. To this end, we consider the Chang version of the weighted Palais-Smale condition…

We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…

We prove a Desch-Schappacher type perturbation theorem for one-parameter semigroups on Banach spaces which are not strongly continuous for the norm, but possess a weaker continuity property. In this paper we chose to work in the framework…

We initiate the study of fine $p$-(super)minimizers, associated with $p$-harmonic functions, on finely open sets in metric spaces, where $1 < p < \infty$. After having developed their basic theory, we obtain the $p$-fine continuity of the…

We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variational problems, we consider group actions…

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…

We show that the ultralimit of a bounded sequence of Lipschitz maps into pointed metric spaces extends naturally to $p$-bounded sequences of Sobolev maps and that this ultralimit for Sobolev maps enjoys desirable properties. We use this to…

In an infinite dimensional Hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields. We prove that one can construct by the…