In this paper, a new algorithm for solving a class of variational inclusions involving H-monotone operators is considered in Hilbert spaces. We investigate a general iterative algorithm, which consists of a resolvent operator technique step followed by a suitable projection step. We prove the convergence of the algorithm for a maximal monotone operator without Lipschitz continuity. These result...

We estimate the decay of correlations for some Markov maps on a countable states space. A necessary and suucient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of nitely many cylinders. Estimates are giv...

In this paper, we propose a method for estimating the Sobolev-type embedding constant fromW1,q( ) to Lp( ) on a domain ⊂Rn (n = 2, 3, . . . ) with minimally smooth boundary (also known as a Lipschitz domain), where p ∈ (n/(n – 1),∞) and q = np/(n + p). We estimate the embedding constant by constructing an extension operator fromW1,q( ) toW1,q(Rn) and computing its operator norm. We also present...

We consider a nonlinear (possibly) degenerate elliptic operator Lv = − div a(∇v) + b(x, v) where the functions a and b are, unnecessarly strictly, monotonic. For a given boundary datum φ we prove the existence of the maximum and the minimum of the solutions and formulate a Haar-Rado type result, namely a continuity property for these solutions that may follow from the continuity of φ. In the ho...

In this paper, the authors first discuss characterization of Herz Triebel–Lizorkin spaces with variable exponent via two families operators. By characterization, prove that Lipschitz commutators sublinear operators is bounded from to exponent. As applications, corresponding boundedness estimates for maximal operator, Riesz potential operator and Calderón–Zygmund are established.

We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit $\mathcal{C}^{1,1}$-parametrization and they solve the geodesic equation in sense of Filippov this parametrization. Our proof shows are either everywhere lightlike or timelike. Furthermore, demonstrates an $\alpha$-H\"older $\mathcal{C}^{1,\frac{\alpha}{4}}$-parametrization.

Let S = {St}t≥0 be the semigroup generated on L2(R ) by a selfadjoint, second-order, divergence-form, elliptic operator H with Lipschitz continuous coefficients. Further let Ω be an open subset of R with Lipschitz continuous boundary ∂Ω. We prove that S leaves L2(Ω) invariant if, and only if, the capacity of the boundary with respect to H is zero or if, and only if, the energy flux across the b...

Nonsmooth operator equations in function spaces are considered, which depend on perturbation parameters. The nonsmoothness arises from a projection onto an admissible interval. Lipschitz stability in L∞ and Bouligand differentiability in L of the parameter-to-solution map are derived. An adjoint problem is introduced for which Lipschitz stability and Bouligand differentiability in L∞ are obtain...

We present an operator space version of Rieffel’s theorem on the agreement of the metric topology, on a subset of the Banach space dual of a normed space, from a seminorm with the weak*-topology. As an application we obtain a necessary and sufficient condition for the matrix metric from an unbounded Fredholm module to give the BW-topology on the matrix state space of the C-algebra. Motivated by...

This paper is concerned with an explicit value of the embedding constant from [Formula: see text] to [Formula: see text] for a domain [Formula: see text] ([Formula: see text]), where [Formula: see text]. We previously proposed a formula for estimating the embedding constant on bounded and unbounded Lipschitz domains by estimating the norm of Stein's extension operator. Although this formula can...