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A well-defined local continuum damage model with softening via convexification and entropic regularization

Lauff C, Schlichting A, Böhlke T, Schneider M.   +3 more
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Critical point equation on four‐dimensional compact manifolds

Mathematische Nachrichten, 2014
The aim of this article is to study the space of metrics with constant scalar curvature of volume 1 that satisfies the critical point equation for simplicity CPE metrics. It has been conjectured that every CPE metric must be Einstein. Here, we shall focus our attention for 4‐dimensional half conformally flat manifolds M4.
Barros, Abdênago, Ribeiro, Ernani jun.
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Critical Point Equation on Almost Kenmotsu Manifolds

Ukrainian Mathematical Journal, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
De, U. C., Mandal, K.
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A study of critical point equation and *-critical point equation on Sasakian manifolds

International Journal of Geometric Methods in Modern Physics, 2022
In this paper, we initiate the study of critical point equation and *-critical point equation within the substructure of Sasakian manifolds. We prove that if a compact Sasakian manifold admits CPE, then either the manifold is Einstein or the potential function is harmonic in an open subset.
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*- Critical point equation on N(k)-contact manifolds

SERIES III - MATEMATICS, INFORMATICS, PHYSICS, 2020
The object of the present paper is to characterize N(k)-contact metric manifolds satisfying the *-critical point equation. It is proved that, if (g, λ) is a non-constant solution of the *-critical point equation of a non-compact N(k)-contact metric manifold, then (1) the manifold M is locally isometric to the Riemannian product of a at (n + 1 ...
D. Dey, P. Majhi
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Rigidity of the critical point equation

Mathematische Nachrichten, 2010
AbstractOn a compact n ‐dimensional manifold M, it was shown that a critical point metric g of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satisfies the critical point equation ([5], p. 3222). In 1987 Besse proposed a conjecture in his book [1], p.
Hwang, Seungsu, Chang, Jeongwook, Yun, Gabjin   +2 more
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Equation of state from triple point to critical point

Physics Letters A, 1972
Abstract The droplet model is shown to agree within 1% in the quantity 1⩾ P ϱkT ⪆ 1 4 with experiment for CO 2 - and H 2 O- vapors between the triple and the critical temperature.
W. Rathjen, D. Stauffer, C.S. Kiang
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On the Critical Point Regularity for Degenerate Diffusive Equations

Archive for Rational Mechanics and Analysis, 2022
This article investigates regularity estimates at interior critical points of solutions to degenerate elliptic equations in a heterogeneous medium of type \(-\mathrm{div}(a(x, Du))=f(x,u)\) in \(B_1\subset \mathbb{R}^d\), where \(a:B_1\times \mathbb{R}^d\to \mathbb{R}^d\) satisfies some standard growth and ellipticity assumptions that include the \(p\)-
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Differential Equations with Fixed Critical Points

Annali di Matematica Pura ed Applicata, 1964
To study the integrals of an ordinary differential equation or of a system of such equations is the object of the “analytical theory of differential equations” (d.e.). From this viewpoint, the theory of ordinary of d.e. is a chapter of the theory of analytic functions of a complex variable.
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