Search results for "PSC"
showing 10 items of 183 documents
Some remarks on nonsmooth critical point theory
2006
A general min-max principle established by Ghoussoub is extended to the case of functionals f which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, when f satisfies a compactness condition weaker than the Palais-Smale one, i.e., the so-called Cerami condition. Moreover, an application to a class of elliptic variational-hemivariational inequalities in the resonant case is presented. © Springer Science+Business Media B.V. 2007.
Nowhere differentiable intrinsic Lipschitz graphs
2021
We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher theorem for intrinsic Lipschitz graphs.
RADEMACHER'S THEOREM IN BANACH SPACES WITHOUT RNP
2017
Abstract We improve a Duda’s theorem concerning metric and w *-Gâteaux differentiability of Lipschitz mappings, by replacing the σ-ideal 𝓐 of Aronszajn null sets [ARONSZAJN, N.: Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147–190], with the smaller σ-ideal 𝓐 of Preiss-Zajíček null sets [PREISS, D.—ZAJÍČEK, L.: Directional derivatives of Lipschitz functions, Israel J. Math. 125 (2001), 1–27]. We also prove the inclusion C̃ o ⊂ 𝓐, where C̃ o is the σ-ideal of Preiss null sets [PREISS, D.: Gâteaux differentiability of cone-monotone and pointwise Lipschitz functions, Israel J. Math. 203 (2014), 501–534].
Cheeger-harmonic functions in metric measure spaces revisited
2014
Abstract Let ( X , d , μ ) be a complete metric measure space, with μ a locally doubling measure, that supports a local weak L 2 -Poincare inequality. By assuming a heat semigroup type curvature condition, we prove that Cheeger-harmonic functions are Lipschitz continuous on ( X , d , μ ) . Gradient estimates for Cheeger-harmonic functions and solutions to a class of non-linear Poisson type equations are presented.
On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients
2017
International audience; The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space problem we establish energy estimates with finite loss of derivatives, which is linearly increasing in time. This implies well-posedness in H ∞ , if the coefficients enjoy enough smoothness in x. From this result, by standard arguments (i.e. extension and convexification) we deduce also local existence and uniqueness. A huge part of the analysis is devoted to give an appropriate sense to the Cauchy problem, which is not evide…
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
2013
In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.
TRPV1 channels in nitric oxide-mediated signalling: insight on excitatory transmission in rat CA1 pyramidal neurons
2022
Nitric oxide (NO) is a fascinating signalling molecule implicated in a plethora of biological functions, especially at the synaptic level. Exploring neurotransmission in the hippocampus could be instrumental in the individuation of putative targets for nitric-oxide mediated neuromodulation, especially in terms of the potential repercussions on fundamental processes i.e. synaptic plasticity and excitability-related phenomena. Among these targets, endovanilloid signalling constitutes an object of study since Transient Receptors Vanilloid type 1 (TRPV1) channels possess a NO-sensitive gate modulating its activation. Also, NO has been referred to as a mediator for numerous endocannabinoid effec…
Alginate-Agarose Hydrogels Improve the In Vitro Differentiation of Human Dental Pulp Stem Cells in Chondrocytes. A Histological Study
2021
[EN] Matrix-assisted autologous chondrocyte implantation (MACI) has shown promising results for cartilage repair, combining cultured chondrocytes and hydrogels, including alginate. The ability of chondrocytes for MACI is limited by different factors including donor site morbidity, dedifferentiation, limited lifespan or poor proliferation in vitro. Mesenchymal stem cells could represent an alternative for cartilage regeneration. In this study, we propose a MACI scaffold consisting of a mixed alginate-agarose hydrogel in combination with human dental pulp stem cells (hDPSCs), suitable for cartilage regeneration. Scaffolds were characterized according to their rheological properties, and their…
Relaxation of Quasilinear Elliptic SystemsviaA-quasiconvex Envelopes
2002
We consider the weak closure WZof the set Z of all feasible pairs (solution, flow) of the family of potential elliptic systems div s0 s=1 s(x)F 0 s(ru(x )+ g(x)) f(x) =0i n; u =( u1;:::;um)2 H 1 0 (; R m ) ; =( 1;:::;s 0 )2 S; where R n is a bounded Lipschitz domain, Fs are strictly convex smooth functions with quadratic growth and S =f measurable j s(x )=0o r 1 ;s =1 ;:::;s0 ;1(x )+ +s0 (x )=1 g .W e show that WZis the zero level set for an integral functional with the integrand QF being the A-quasiconvex envelope for a certain functionF and the operator A = (curl,div) m . If the functions Fs are isotropic, then on the characteristic cone (dened by the operator A) QF coincides with the A-p…