Second-order L2L^2-regularity in nonlinear elliptic problems

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the existence and square integrability of the weak derivatives of the nonlinear expression of the gradient under the divergence operator. This provides a nonlinear counterpart of the classical $L^2$-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are established. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required. If the domain is convex, no regularity of its boundary is needed at all

Genetic evidence of two sibling species within the Contracoecum ogmorhini Johnson & Mawson 1941 complex (Nematoda; Anisakidae) from otariid seals in boreal and austral regions

Genetic variation of Contracaecum ogmorhini (sensu lato) populations from different otariid seals of the northern and southern hemisphere was studied on the basis of 18 enzyme loci as well as preliminary sequence analysis of the mitochondrial cyt b gene (260 bp). Samples were collected from Zalophus californianus in the boreal region and from Arctocephalus pusillus pusillus, A. pusillus doriferus and A. australis from the austral region. Marked genetic heterogeneity was found between C. ogmorhini (sensu lato) samples from the boreal and austral region, respectively. Two loci (Mdh-2 and NADHdh) showed fixed differences and a further three loci (Iddh, Mdh-1 and 6Pgdh) were highly differentiated between boreal and austral samples. Their average genetic distance was DNei = 0.36 at isozyme level. At mitochondrial DNA level, an average proportion of nucleotide substitution of 3.7% was observed. These findings support the existence of two distinct sibling species, for which the names C. ogmorhini (sensu stricto) and C. margolisi n. sp., respectively, for the austral and boreal taxon, are proposed. A description for C. margolisi n. sp. is provided. No diagnostic morphological characters have so far been detected; on the other hand, two enzyme loci, Mdh-2 and NADHdh, fully diagnostic between the two species, can be used for the routine identification of males, females and larval stages. Mirounga leonina was found to host C. ogmorhini (s.s.) inmixed infections with C. osculatum (s.l.) (of which C. ogmorhini (s.l.) was in the past considered to be a synonym) and C. miroungae; no hybrid genotypes were found,confirming the reproductive isolation of these three anisakid species. The hosts and geographical range so far recorded for C. margolisi n. sp. and C. ogmorhini (s.s.) are given

Lattice Boltzmann method for warm fluid simulations of plasma wakefield acceleration

A comprehensive characterization of lattice Boltzmann (LB) schemes to perform warm fluid numerical simulations of particle wakefield acceleration (PWFA) processes is discussed in this paper. The LB schemes we develop hinge on the moment matching procedure, allowing the fluid description of a warm relativistic plasma wake generated by a driver pulse propagating in a neutral plasma. We focus on fluid models equations resulting from two popular closure assumptions of the relativistic kinetic equations, i.e., the local equilibrium and the warm plasma closure assumptions. The developed LB schemes can, thus, be used to disclose insights on the quantitative differences between the two closure approaches in the dynamics of PWFA processes. Comparisons between the proposed schemes and available analytical results are extensively addressed

Frontiers of beam diagnostics in plasma accelerators: measuring the ultra-fast and ultra-cold

Advanced diagnostics are essential tools in the development of plasma-based accelerators. The accurate measurement of the quality of beams at the exit of the plasma channel is crucial to optimize the parameters of the plasma accelerator. 6D electron beam diagnostics will be reviewed with emphasis on emittance measurement, which is particularly complex due to large energy spread and divergence of the emerging beams, and on femtosecond bunch length measurements

An estimate for the Morse index of a Stokes wave

Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler-Lagrange equation of a certain functional. This allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.Comment: This version contains an additional reference and some minor change

High quality superconducting niobium films produced by Ultra High Vacuum Cathodic Arc

The vacuum arc is a well-known technique to produce coating with enhanced adhesion and film density. Many cathodic arc deposition systems are actually in use in industry and research. They all work under (high) vacuum conditions in which water vapor pressure is an important source of film contamination, especially in the pulsed arc mode of operation. Here we present a Cathodic Arc system working under Ultra High Vacuum conditions (UHVCA). UHVCA has been used to produce ultra-pure niobium films with excellent structural and electrical properties at a deposition temperature lower than 100oC. The UHVCA technique therefore opens new perspectives for all applications requiring ultra-pure films or, as in the case of Plasma Immersion Ion Implantation, ultra-pure plasmas.Comment: submitted to AP

Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas