We examine solutions u = PI f to ∆u − V u = 0 on a Lipschitz domain Ω in a compact Riemannian manifold M , satisfying u = f on ∂Ω, with particular attention to ranges of (s, p) for which one has Besov-to-L-Sobolev space results of the form PI : B s (∂Ω) −→ Lps+1/p(Ω), and variants, when the metric tensor on M has limited regularity, described by a Hölder or a Dini-type modulus of continuity. We...

We study the applicability of the the method of layer potentials, in the treatment of boundary value problems for the Laplace-Beltrami operator on Lipschitz subdomains of Riemannian manifolds, in the case when metric tensor gjkdxj ⊗ dxk has low regularity. Under the assumption that |gjk(x) − gjk(y)| ≤ C ω(|x − y|), where the modulus of continuity ω satisfies a Dini type condition, we prove the ...

Consider the linear parabolic operator in divergence form Hu = ∂tu(X, t)− div(A(X)∇u(X, t)). We employ a method of Dahlberg to show that the Dirichlet problem forH in the upper half plane is well-posed for boundary data in Lp, for any elliptic matrix of coefficients A which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation ...

Abstract. Let TΩ,α (0 ≤ α < n) be the singular and fractional integrals with variable kernel Ω(x,z), and [b,TΩ,α ] be the commutator generated by TΩ,α and a Lipschitz function b. In this paper, the authors study the boundedness of [b,TΩ,α ] on the Hardy spaces, under some assumptions such as the Lr-Dini condition. Similar results and the weak type estimates at the end-point cases are also given...

In this paper we first provide a general formula of inclusion for the DiniHadamard ε-subdifferential of the difference of two functions and show that it becomes equality in case the functions are directionally approximately starshaped at a given point and a weak topological assumption is fulfilled. To this end we give a useful characterization of the Dini-Hadamard ε-subdifferential by means of ...

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gâteaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key elem...

In Escherichia coli, the SOS response is induced upon DNA damage and results in the enhanced expression of a set of genes involved in DNA repair and other functions. The initial step, self-cleavage of the LexA repressor, is promoted by the RecA protein which is activated upon binding to single-stranded DNA. In this work, induction of the SOS response by the addition of mitomycin C was found to ...