Variational Methods in Mathematical Physics

Blanchard, Philippe; Brüning, Erwin

doi:10.1007/978-3-642-82698-6

Cited by 116 publications

(137 citation statements)

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“…Combining this theorem with the cg-Hohenberg-Kohn Theorem gives Gâteaux differentiability [9,11,13] of the restriction of F L to X N .…”

Section: Theorem 32 (Existence Of Levy Search Solutions)mentioning

confidence: 99%

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Coarse-grained V representability

Lammert

2006

The Journal of Chemical Physics

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The unsolved problem of determining which densities are ground state densities of an interacting electron system in some external potential is important to the foundations of density functional theory. A coarse-grained version of this ensemble V-representability problem is shown to be thoroughly tractable. Averaging the density of an interacting electron system over the cells of a regular partition of space produces a coarse-grained density. It is proved that every strictly positive coarsegrained density is coarse-grained ensemble V-representable: there is a unique potential, constant over each cell of the partition, which has a ground state with the prescribed coarse-grained density. For a system confined to a box, the (coarse-grained) Lieb functional is also shown to be Gâteaux differentiable. All results extend to open systems.

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“…Combining this theorem with the cg-Hohenberg-Kohn Theorem gives Gâteaux differentiability [9,11,13] of the restriction of F L to X N .…”

Section: Theorem 32 (Existence Of Levy Search Solutions)mentioning

confidence: 99%

“…(13). Since e −x is a bounded function on x > 0, e −H(v α ) → e −H(v) in strong operator topology (RS:VIII.20, or W:Thm.…”

Section: Theorem 42 (Existence Of Levy Search Solutions)mentioning

confidence: 99%

Coarse-grained V representability

Lammert

2006

The Journal of Chemical Physics

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“…The periodic spectrum consists of periodic eigenvalues (numbers λ for which there is a periodic eigenfunction: ψ(0) = ψ (1) and ψ x (0) = ψ x (1)) and antiperiodic eigenvalues (numbers λ for which there is an antiperiodic eigenfunction:…”

Section: Isospectral Problemmentioning

confidence: 99%

Stability for the periodic Camassa-Holm equation

Lenells¹

2005

MATH. SCAND.

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“…In particular, we prove that the reference configuration is stable when the coupling coefficient lies in a suitable subset of the open interval (K sf 1 , K sf 2 ). The mathematical reasoning parallels that given, for example, in [12]. That is, for the reference configuration to be stable, thesecond derivative of E tot by means of a suitable eigenvalue problem, the proper quadratic form is…”

Section: Stability Of the Stressed Reference Configurationmentioning

confidence: 69%

Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid

Sciarra

Batra²,

Dell’Isola³

2003

Journal of Elasticity

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Abstract. We study infinitesimal deformations of a porous linear elastic body saturated with an inviscid fluid and subjected to conservative surface tractions. The gradient of the mass density of the solid phase is also taken as an independent kinematic variable and the corresponding higher-order stresses are considered. Balance laws and constitutive relations for finite deformations are reduced to those for infinitesimal deformations, and expressions for partial surface tractions acting on the solid and the fluid phases are derived. A boundary-value problem for a long hollow porous solid cylinder filled with an ideal fluid is solved, and the stability of the stressed reference configuration with respect to variations in the values of the coefficient coupling deformations of the two phases is investigated. An example of the problem studied is a cylindrical cavity leached out in salt formations for storing hydrocarbons.Key words: solid-fluid mixture, conservative tractions, principle of virtual power, partial tractions, fluid-filled cylindrical cavity, stability analysis. R.C. Batra dedicates this work with deep respect and admiration to

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Variational Methods in Mathematical Physics

Cited by 116 publications

References 0 publications

Coarse-grained V representability

Coarse-grained V representability

Stability for the periodic Camassa-Holm equation

Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid

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