相关论文: An extrapolation result in the variational setting…

In this paper we introduce Calder\'on-Zygmund theory for singular stochastic integrals with operator-valued kernel. In particular, we prove $L^p$-extrapolation results under a H\"ormander condition on the kernel. Sparse domination and sharp…

We remove the semisimple condition in the mod-$p$ local-global compatibility result of arXiv:2106.10674. Namely, assuming flatness of $\pi_{\mathfrak{m}}^\vee$ and $\overline{\sigma}_{\mathfrak{m}}|_{\mathrm{Gal}_{F^+_{\mathfrak{p}}}}$…

We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…

We discuss the interrelations between various basis set extrapolation formulas and show that for the nZaPa and aug-cc-pVnZ basis set formulas, for n=4--6 their behavior closely resembles the Petersson (L+a)^{-3} formula with a shift a…

Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…

In this paper we consider and generalize a model, recently proposed and analytically investigated in its quasi-stationary approximation by the authors, for visco-elasticity with large deformations and conditional compatibility, where the…

The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…

We prove the global existence of the solution for fractional Hartree equations with initial data in certain real interpolation spaces between $L^{2}$ and some kinds of new function spaces defined by fractional Schr\"odinger semigroup, which…

We establish the local H\"older regularity of the spatial gradient of bounded weak solutions $u\colon E_T\to\R^k$ to the non-linear system of parabolic type \begin{equation*} \partial_tu-\Div\Big(…

A DualTPD method is proposed for solving nonlinear partial differential equations. The method is characterized by three main features. First, decoupling via Fenchel--Rockafellar duality is achieved, so that nonlinear terms are discretized…

In this paper, we study the existence of random periodic solutions for semilinear SPDEs on a bounded domain with a smooth boundary. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations…

The seminal paper of Daubechies, Defrise, DeMol made clear that $\ell^p$ spaces with $p\in [1,2)$ and $p$-powers of the corresponding norms are appropriate settings for dealing with reconstruction of sparse solutions of ill-posed problems…

In this paper we prove quantitative regularity results for stationary and minimizing extrinsic biharmonic maps. As an application, we determine sharp, dimension independent $L^p$ bounds for $\nabla^k f$ that do not require a small energy…

We prove a higher regularity result for weak solutions to nonlinear nonlocal equations along the integrability scale of Bessel potential spaces $H^{s,p}$ under a mild continuity assumption on the kernel. By embedding, this also yields…

This paper introduces a new $p$-dependent coercivity condition through which $L^p$-moments for solutions can be obtained for a large class of SPDEs in the variational framework. If $p=2$, our condition reduces to the classically coercivity…

We derive a general theorem relating the energy, momentum and velocity of any solitary wave solution of the generalized KdV equation which enables us to relate the amplitude, width, and momentum to the velocity of these solutions. We obtain…

We study the second-order quasi-linear stochastic partial differential equations (SPDEs) defined on $C^1$ domains. The coefficients are random functions depending on $t,x$ and the unknown solutions. We prove the uniqueness and existence of…

These notes present an alternative approach to the asymptotic stability of stochastic partial differential equations driven by multiplicative noise, applicable to a wide range of dissipative systems. The method builds on general criteria…

This paper is devoted to rigidity results for some elliptic PDEs and related interpolation inequalities of Sobolev type on smooth compact connected Riemannian manifolds without boundaries. Rigidity means that the PDE has no other solution…

In a previous paper we developed a regularity and compactness theory in Euclidean ambient spaces for codimension 1 weakly stable CMC integral varifolds satisfying two (necessary) structural conditions. Here we generalize this theory to the…