Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness their solutions established under boundary conditions Dirichlet, or Neumann, Robin type. A decisive role the results played optimal forms Orlicz-Sobolev embeddings and trace embeddings, which all...

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ sequence spaces over p−metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform ∆2 condition, and we also discuss some topological properties of the resulting spaces of χ with respect to ideal structures which is solid and monotone. Hence, g...

converge a.e. for all f in L log log(L) but fail to have a finite limit for an f ∈ L. In fact, we show that for each Orlicz space properly contained in L, 1 ≤ q < ∞, there is a sequence along which the ergodic averages converge for functions in the Orlicz space, but diverge for all f ∈ L . This extends the work of K. Reinhold, who, building on the work of A. Bellow, constructed a sequence for w...

Many types of insurance premium principles and/or risk measures can be characterized by means of a set of axioms, which in many cases are rather arbitrarily chosen and not always in accordance with economic reality. In the present paper we generalize Yaari’s risk measure by relaxing his axioms. In addition, we derive translation invariant minimal Orlicz risk measures, which we call Haezendonck ...

In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations. We employ the direct method of the calculus of variations, i.e. we obtain solutions minimizing certain functional I. We give conditions which ensure that I is finitely defined and differentiable on certain subsets of Orlicz-Sobolev spaces W L associated to an N -function Φ. We show that, in ...

Here, Ω is a bounded domain with sufficiently smooth (e.g. Lipschitz) boundary ∂Ω and ∂/∂ν denotes the (outward) normal derivative on ∂Ω. We assume that the function φ :R→R, defined by φ(s)= α(|s|)s if s = 0 and 0 otherwise, is an increasing homeomorphism from R to R. Let Φ(s)= ∫ s 0 φ(t)dt, s∈R. Then Φ is a Young function. We denote by LΦ the Orlicz space associated withΦ and by ‖ · ‖Φ the usu...

1. Let us recall the basic definitions of the theory of Orlicz spaces (see, for example, [1]). Henceforth (Ω,A, μ) is the triple consisting of a set Ω, σ-algebra A of its subsets and a σ-additive measure μ defined on A. It is assumed that μ is continuous on Ω (that is any set of positive measure can be divided into two sets of equal measures) and is finite: μ(Ω) < ∞. Let M : [0,+∞) → [0,+∞) be ...

We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on Orlicz hearts. In addition, we obtain its representation with the minimal pen...