Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold M. Under the assumption that the sectional curvature of M is strictly positive, we prove the existence of a smoothly immersed sphere minimizing the L^{2} integral of the second fundamental form. Assuming instead that the sectional curvature is less than or equal to 2, and that there exists a point in M with scalar curvature bigger than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1, where H is the mean curvature vector

A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

Regularity of solutions to higher-order integrals of the calculus of variations

We obtain new regularity conditions for problems of calculus of variations with higher-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main regularity result asserts that autonomous integral functionals with a Lagrangian having coercive partial derivatives with respect to the higher-order derivatives admit only minimizers with essentially bounded derivatives

Construction of Lp\mathcal L^p-strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions

We provide a general construction scheme for $\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated semigroup and resolvents of kernels having the $\mathcal L^p$-strong Feller property. They allow us to construct a process which solves the corresponding martingale problem for all starting points from a known set, namely the set where the regularity assumptions hold. We apply this result to construct elliptic diffusions having locally Lipschitz matrix coefficients and singular drifts on general open sets with absorption at the boundary. In this application elliptic regularity results imply the desired regularity assumptions

Minimally Invasive Surgical Approaches and Traditional Total Hip Arthroplasty: A Meta-Analysis of Radiological and Complications Outcomes

BACKGROUND: Minimally invasive total hip arthroplasty (MITHA) remains considerably controversial. Limited visibility and prosthesis malposition increase the risk of post-surgical complications compared to those of the traditional method. METHODS: A meta-analysis was undertaken of all published databases up to May 2011. The studies were divided into four subgroups according to the surgical approach taken. The radiological outcomes and complications of minimally invasive surgery were compared to traditional total hip arthroplasty (TTHA) using risk ratio, mean difference, and standardized mean difference statistics. RESULTS: In five studies involving the posterolateral approach, no significant differences were found between the MITHA groups and the TTHA groups in the acetabular cup abduction angle (p = 0.41), acetabular anteversion (p = 0.96), and femoral prosthesis position (p = 0.83). However, the femoral offset was significantly increased (WMD = 3.00; 95% CI, 0.40-5.60; p = 0.02). Additionally, there were no significant differences among the complications in both the groups (dislocations, nerve injury, infection, deep vein thrombosis, proximal femoral fracture) and revision rate (p>0.05). In three studies involving the posterior approach, there were no significant differences in radiological outcomes or all other complications between MITHA or TTHA groups (p>0.05). Three studies involved anterolateral approach, while 2 studies used the lateral approach. However, the information from imaging and complications was not adequate for statistical analysis. CONCLUSIONS: Posterior MITHA seems to be a safe surgical procedure, without the increased risk of post-operative complication rates and component malposition rates. The posterolateral approach THA may lead to increased femoral offset. The current data are not enough to reach a positive conclusion that lateral and anterolateral approaches will result in increased risks of adverse effects and complications at the prosthesis site

Variable exponent Besov-Morrey spaces

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe