1,720,972 research outputs found
Completeness theorems for the Stokes system
Full text linkThe linear Stokes system is considered and the completeness (in the sense of Picone) on the boundary of a given bounded domain of polynomial solutions is proved. The completeness is obtained in both and uniform norms
Criterion for the functional dissipativity of second order differential operators with complex coefficients
No full textIn the present paper we consider the Dirichlet problem for the second order differential operator E = ∇(A ∇), where A is a matrix with complex valued L^∞ entries. We introduce the concept of dissipativity of E with respect to a given function φ : R+ → R+. Under the assumption that the ImA is symmetric, we prove that the condition |sφ′(s)| |⟨ImA (x)ξ, ξ⟩| ⩽ 2√φ(s)[sφ(s)]′ ⟨ReA (x)ξ, ξ⟩ (for almost every x∈Ω⊂R^N) and
for any s>0,ξ∈^R^N) is necessary and sufficient for the functional dissipativity of E
Some new applications of the theory of conjugate differential forms
No full textIn this survey we describe two applications of the concept of conjugate differential forms. Namely, after describing the concept of conjugate and selfconjugate differential forms, we consider an extension of the Brothers Riesz Theorem to higher real dimension and Riesz type inequalities for differential forms
The -dissipativity of first order partial differential operators
Full text linkWe find necessary and sufficient conditions for the (Formula presented.)-dissipativity of the Dirichlet problem for systems of partial differential operators of the first order with complex locally integrable coefficients. As a by-product we obtain sufficient conditions for a certain class of systems of the second order
Criterion for the functional dissipativity of the Lamé operator
No full textAfter introducing the concept of functional dissipativity of the Dirichlet problem in a domain for systems of partial differential operators of the form
\{A_{hk}\}mxmL^\infty$ entries), we find necessary and sufficient conditions for the functional dissipativity of the two-dimensional Lamé system. As an application of our theory we provide two regularity results for the displacement vector in the N-dimensional equilibrium problem, when the body is fixed along its boundary
On the traction problem for steady elastic oscillations equations: the double layer potential ansatz
Full text linkThe three-dimensional traction problem for steady elastic oscillations equations is studied. Representability of its solution by means of a double layer potential is considered instead of the more usual simple layer potential
The Simple-Layer Potential Approach to the Dirichlet Problem: An Extension to Higher Dimensions of Muskhelishvili Method and Applications
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On the double layer potential ansatz for the n-dimensional Helmholtz equation with Neumann condition
Full text linkIn the present paper we consider the Neumann problem for the ndimensional Helmholtz equation. In particular we deal with the problem of representability of the solutions by means of double layer potentials
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