In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent inequality. While the principle of independent interest, it employed in paper provide an elementary proof solution existence Theoretical results illustrated applications two contact problems.

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular many areas of statistics and machine learning. give first minimax-optimal rates for this problem general distances two classes densities: smooth densities [0,1]d bounded away from 0, sub-Gaussian lying Hölder class Cs, s∈(0,1). Unlike classical es...

We extend Fano’s inequality, which controls the average probability of (disjoint) events in terms of the average of some Kullback-Leibler divergences, to work with arbitrary [0, 1]–valued random variables. Our simple two-step methodology is general enough to cover the case of an arbitrary (possibly continuously infinite) family of distributions as well as [0, 1]–valued random variables not nece...

We give a comprehensive theoretical characterization of a nonparametric estimator for the L2 divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is √ n-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically normal, construct asymptotic confidence int...

In this paper, we give two new existence theorems for maximal elements in H-spaces. As their applications, we obtain a extended version of Fan–Yen minimax inequality and some new existence theorems of an equilibrium for a qualitative game and an abstract economy. Our main results not only generalize the corresponding results of [4, 12, 15, 16] to H-spaces, but also the open question raised by Y...

We study nonlinear eigenvalue problems of the type −div(a(x)∇u) = g(λ,x,u) in RN , where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequal...