1,720,976 research outputs found
Invertibility of Orlicz–Sobolev Maps
No full textWe extend the global invertibility result (Henao et al., Adv Calculus Var 14(2):207–230, 2021) to a class of orientation-preserving Orlicz–Sobolev maps with an integrability just above n − 1, whose traces on the boundary are also Orlicz–Sobolev and which do not present cavitation in the interior or at the boundary. As an application, we prove the existence of a.e. injective minimizers within this class for functionals in nonlinear elasticity
Orlicz-Sobolev nematic elastomers
Full text linkWe extend the existence theorems in Barchiesi et al. (2017), for models of nematic
elastomers and magnetoelasticity, to a larger class in the scale of Orlicz spaces.
These models consider both an elastic term where a polyconvex energy density is
composed with an unknown state variable defined in the deformed configuration,
and a functional corresponding to the nematic energy (or the exchange and
magnetostatic energies in magnetoelasticity) where the energy density is integrated
over the deformed configuration. In order to obtain the desired compactness and
lower semicontinuity, we show that the regularity requirement that maps create
no new surface can still be imposed when the gradients are in an Orlicz class with
an integrability just above the space dimension minus one
Partial Regularity for Minimizers of Discontinuous Quasiconvex Integrals with general growth
Full text linkWe prove the partial Hölder continuity for minimizers of quasiconvex functionals
F(u):=∫Ωf(x,u,Du)dx,
where f satisfies a uniform VMO condition with respect to the x-variable and is continuous with respect to u. The growth condition with respect to the gradient variable is assumed a general one
A free discontinuity model for smectic thin films
Full text linkWe attempt to describe surface defects in smectic A thin films by formulating
a free discontinuity problem - that is, a variational problem in which the
order parameter is allowed to have jump discontinuities on some (unknown) set.
The free energy functional contains an interfacial energy which penalizes
dislocations of the smectic layers at the jump. We discuss mathematical issues
related to the existence of minimizers and provide examples of minimizers in
some simplified settings
Boundary Convergence Properties of Lp-AVERAGES
No full textWe study convergence at the boundary of a domain in connection with properties of solutions to dynamic programming principle problems associated with Lp-averages
convergence of natural p-means for the p-Laplacian in the Heisenberg Group
Full text linkIn this paper we prove uniform convergence of approximations to p-harmonic functions by using natural p-mean operators on bounded domains of the Heisenberg group H which satisfy an intrinsic exterior corkscrew condition. These domains include Euclidean C1,1 domains
KFP operators with coefficients measurable in time and Dini continuous in space.
Full text linkWe consider degenerate Kolmogorov–Fokker–Planck operators (Formula presented.) (with (x,t)∈R^N+1 and 1≤m_0≤N) such that the corresponding model operator having constant aij is hypoelliptic, translation invariant w.r.t. a Lie group operation in R^N+1 and 2-homogeneous w.r.t. a family of nonisotropic dilations. The matrix (aij)i,j=1 m^0 is symmetric and uniformly positive on Rm^0. The coefficients aij are bounded and Dini continuous in space, and only bounded measurable in time. This means that, setting (Formula presented.) we require the finiteness of ‖aij‖D(ST). We bound ω_uxixj,ST, ‖u_xixj‖L∞(ST) (i,j=1,2,..,m0), ω_Yu,ST, ‖Yu‖L∞(ST) in terms of ω_Lu,ST, ‖Lu‖L∞(ST) and ‖u‖L∞ST, getting a control on the uniform continuity in space of u_xixj,Yu if Lu is bounded and Dini-continuous in space. Under the additional assumption that both the coefficients aij and Lu are log-Dini continuous, meaning the finiteness of the quantity (Formula presented.) we prove that u_xixj and Yu are Dini continuous; moreover, in this case, the derivatives u_xixj are locally uniformly continuous in space and time
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