347 research outputs found
On the Sobolev trace Theorem for variable exponent spaces in the critical range
In this paper we study the Sobolev Trace Theorem for variable exponent spaces
with critical exponents. We find conditions on the best constant in order to
guaranty the existence of extremals. Then we give local conditions on the
exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to
satisfy such conditions, and therefore to ensure the existence of extremals.Comment: 21 pages, submitte
Existence of solution to a critical equation with variable exponent
In this paper we study the existence problem for the Laplacian
operator with a nonlinear critical source. We find a local condition on the
exponents ensuring the existence of a nontrivial solution that shows that the
Pohozaev obstruction does not holds in general in the variable exponent
setting. The proof relies on the Concentration--Compactness Principle for
variable exponents and the Mountain Pass Theorem
Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces
We study the continuity and compactness of embeddings for radial Besov and
Triebel-Lizorkin spaces with weights in the Muckenhoupt class . The
main tool is a discretization in terms of an almost orthogonal wavelet
expansion adapted to the radial situation
Non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings
Reliable design of industrial components against high cycle multiaxial fatigue requires a model capable of predicting both stress gradient and load type effects. Indeed, taking into account gradient effects is of prior importance for the applicability of fatigue models to real structures. In this paper, a fatigue life assessment method is proposed for proportional and non-proportional multiaxial variable amplitude loadings in the range 104 –107 cycles. This method derives from the fatigue criterion initially proposed by Palin-Luc and Lasserre (1998) [2] and revisited by Banvillet et al. (2003) [16] for multiaxial constant amplitude loading. The new proposal consists of a complete reformulation and extension of the previ- ously cited energy based fatigue strength criteria. It includes two major improvements of the existing criteria. The first one consists in a fatigue criterion for multiaxial variable amplitude loadings while only constant amplitude loadings were considered in the above cited works. The second one is an extension to an incremental fatigue life assessment method for proportional and non-proportional multiaxial variable amplitude loadings. No cycle counting technique is needed whatever the variable amplitude load- ings type considered (uniaxial or multiaxial). The predictions of the method for constant and variable amplitude multiaxial loadings are compared with experimental results on specimens from literature and from new experiments on a ferrito-perlitic steel. The above mentioned method has been implemented as a post-processor of a finite element software. An application to a railway wheel is finally presented.Thèse CIFRE avec la SNCF, contrat direct ARTS / SNC
- …