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In this paper, we study the least squares estimator for sublinear expectations. Under some mild assumptions, we prove the existence and uniqueness of the least squares estimator. The relationship between the least squares estimator and the conditional coherent risk measure (resp. the conditional g -expectation) is also explored. Then some characterizations of the least squares estimator are given. [ABSTRACT FROM AUTHOR]

In this paper, we prove nonexistence of positive supersolutions of a semilinear equation − div ( A ( x ) ∇ u ) + b ( x ) ⋅ ∇ u = f ( u ) in exterior domains in R n ( n ≥ 3 ), where A ( x ) is bounded and uniformly elliptic, b ( x ) = O ( | x | − 1 ) , div b = 0 and f is a continuous and positive function in ( 0 , ∞ ) satisfying f ( u ) ∼ u q as u → 0 with q ≤ n / ( n − 2 ) . Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions. [ABSTRACT FROM AUTHOR]

The paper considers systems of the form − div ( | ∇ u | n − 2 ∇ u ) = | ∇ u | n − 2 Ω ⋅ ∇ u on a bounded domain in R n with u ∈ W 1 , n , a matrix Ω ∈ L n (depending on u ) and some additional structural assumptions on Ω. We prove that if a sequence of solutions of the above system converges weakly, the limit itself is also a solution. The class of systems considered includes the n -harmonic system and the presented reasoning is a generalization of C. Wang's proof for n -harmonic maps. [ABSTRACT FROM AUTHOR]

In this paper, we study the initial and boundary value problem of the Navier–Stokes equations in the half-space. We prove the existence of weak solution u ∈ L α q ( 0 , ∞ ; L p ( R + n ) ) , α = 1 2 ( 1 − n p − 2 q ) ≥ 0 , n < p < ∞ with ∇ u ∈ L loc q 2 ( 0 , ∞ ; L loc p 2 ( R + n ) ) for the solenoidal initial data h ∈ B ˙ p q − 1 + n p ( R + n ) and the boundary data g ∈ L α q ( 0 , ∞ ; B ˙ p p − 1 p ( R n − 1 ) ) when ‖ h ‖ B ˙ p q − 1 + n p ( R + n ) + ‖ g ‖ L α q ( 0 , ∞ ; B ˙ p p − 1 p ( R n − 1 ) ) is small enough. Moreover, the solution is unique in the class L α q ( 0 , T ; L p ( R + n ) ) for any T ≤ ∞ if α > 0 and for some T < ∞ if α = 0 . [ABSTRACT FROM AUTHOR]

In this paper we prove that spectral synthesis holds for a variety on an Abelian group if spectral analysis holds on it and the residue ring of the annihilator of the variety is a Noether ring. This extends the fundamental result of M. Lefranc about spectral synthesis on finitely generated Abelian groups. [ABSTRACT FROM AUTHOR]

This paper addresses the properties of the C 0 -semigroup generated by the reparable system with finite repair time. In particular, it can be shown that the C 0 -semigroup is eventually differentiable and eventually compact, which is not true for the case when the repair time is infinite, as discussed in [9] and [11] . [ABSTRACT FROM AUTHOR]

This paper is concerned with Wold-type decomposition for regular operators whose orbits under any vector satisfy some growth conditions. Several results on left invertible operators close to isometries are extended. We also give numerous results on the Moore–Penrose inverse for regular operators in this particular setting. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem of the Camassa–Holm equation. We present a well-posedness result and a blow-up criterion of solutions in the inhomogeneous Triebel–Lizorkin spaces. [ABSTRACT FROM AUTHOR]