Related papers: On weak convergence of locally periodic functions
A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.
A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…
A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…
We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their…
We consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity of the optimal value function in dependence of the coupling strength. In order to improve these sensitivity estimates a "coupling adapted" norm…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…
We first establish a local gradient estimate for anisotropic $p$-harmonic functions. A key feature of our estimate is that the constant remains bounded as $p\to 1$; consequently, in the limit $p\to 1$, this estimate yields the local…
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
We consider a combination of local and nonlocal $p$-Laplace equations and discuss several regularity properties of weak solutions. More precisely, we establish local boundedness of weak subsolutions, local H\"older continuity of weak…
Post-selected weak measurement has been widely used in experiments to observe weak effects in various physical systems. However, it is still unclear how large the amplification ability of a weak measurement can be and what determines the…
In this paper we study the mean values of some multiplicative functions connected with the divisor function on the short interval of summation. The asymptocic values for such mean values are proved.
Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems…
We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that…
We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi's counterexample. Here we assume a condition on the support of off-diagonal coefficients…
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 study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…
We start to investigate how small changes on the definition of ordinary means affect their properties. Especially the property of being a mean. In that direction we are looking for weakenings of the basic defining property of means. Hence…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…