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pro vyhledávání: '"Bevan, Jonathan"'
Let $Q$ be a Lipschitz domain in $\mathbb{R}^n$ and let $f \in L^{\infty}(Q)$. We investigate conditions under which the functional $$I_n(\varphi)=\int_Q |\nabla \varphi|^n+ f(x)\,\mathrm{det} \nabla \varphi\, \mathrm{d}x $$ obeys $I_n \geq 0$ for al
Externí odkaz:
http://arxiv.org/abs/2306.11022
Autor:
Dengler, Marcel, Bevan, Jonathan J.
In this paper we consider the problem of minimizing functionals of the form $E(u)=\int_B f(x,\nabla u) \,dx$ in a suitably prepared class of incompressible, planar maps $u: B \rightarrow \mathbb{R}^2$. Here, $B$ is the unit disk and $f(x,\xi)$ is qua
Externí odkaz:
http://arxiv.org/abs/2205.06749
Publikováno v:
In Nonlinear Analysis June 2024 243
In this paper we give an explicit sufficient condition for the affine map $u_\lambda(x):=\lambda x$ to be the global energy minimizer of a general class of elastic stored-energy functionals $I(u)=\int_{\Omega} W(\nabla u)\,dx$ in three space dimensio
Externí odkaz:
http://arxiv.org/abs/1707.08532
Autor:
Shelmerdine, Susan Cheng, Davendralingam, Natasha, Langan, Dean, Palm, Liina, Mangham, Chas, Arthurs, Owen J., CORNRD Study Collaborators, Barber, Joy Louise, Bevan, Jonathan, Choa-Go, Joanna Marie, Colak, Edis, Davies, Thomas, Dodd, Cassandra, Dupre, Mhairi, Edwards, Harriet, Eid, Hadeel, Fagan, Aisling, Gaunt, Trevor, Halliday, Katharine, Hameed, Shema
Publikováno v:
European Radiology; Sep2024, Vol. 34 Issue 9, p5561-5569, 9p
Autor:
Bevan, Jonathan J., Kabisch, Sandra
In this paper we study constrained variational problems that are principally motivated by nonlinear elasticity theory. We examine in particular the relationship between the positivity of the Jacobian $\det \nabla u$ and the uniqueness and regularity
Externí odkaz:
http://arxiv.org/abs/1608.00160
Autor:
Bevan, Jonathan J.
Publikováno v:
Archive for Rational Mechanics and Analysis, 2017
We prove the local H\"{o}lder continuity of strong local minimizers of the stored energy functional \[E(u)=\int_{\om}\lambda |\nabla u|^{2}+h(\det \nabla u) \,dx\] subject to a condition of `positive twist'. The latter turns out to be equivalent to r
Externí odkaz:
http://arxiv.org/abs/1509.08245
In this note we formulate a sufficient condition for the quasiconvexity at $x \mapsto \lambda x$ of certain functionals $I(u)$ which model the stored-energy of elastic materials subject to a deformation $u$. The materials we consider may cavitate, an
Externí odkaz:
http://arxiv.org/abs/1507.02622
Publikováno v:
Proceedings: Mathematical, Physical and Engineering Sciences, 2019 Nov 01. 475(2231), 1-15.
Externí odkaz:
https://www.jstor.org/stable/26875317