Journal: Annali di matematica pura ed applicata

Abbreviation

Ann. mat. pura appl.

Publisher

Springer

Journal Volumes

ISSN

0373-3114
1618-1891

Description

Filters

2012 - 201932020 - 20221
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Publications 1 - 4 of 4
  • A fractional version of Rivière's GL(n)-gauge
    Item type: Journal Article
    Da Lio, Francesca; Mazowiecka, Katarzyna; Schikorra, Armin (2022)
    Annali di matematica pura ed applicata
    We prove that for antisymmetric vector field Ω with small L²-norm there exists a gauge A ∈ L∞ ∩ Ẇ(1/2,2)(ℝ¹, GL(N)) such that div(1/2)(AΩ − d(1/2)A) = 0. This extends a celebrated theorem by Rivière to the nonlocal case and provides conservation laws for a class of nonlocal equations with antisymmetric potentials, as well as stability under weak convergence.
  • Shape derivatives in differential forms I: an intrinsic perspective
    Item type: Journal Article
    Hiptmair, Ralf; Li, Jingzhi (2013)
    Annali di matematica pura ed applicata
    We treat Zolésio’s velocity method of shape calculus using the formalism of differential forms, in particular, the notion of Lie derivative. This provides a unified and elegant approach to computing even higher-order shape derivatives of domain and boundary integrals and avoids the tedious manipulations entailed by classical vector calculus. Hitherto unknown expressions for shape Hessians can be derived with little effort. The perspective of differential forms perfectly fits second-order boundary value problems (BVPs). We illustrate its power by deriving the shape derivatives of solutions to second-order elliptic BVPs with Dirichlet, Neumann and Robin boundary conditions. A new dual mixed variational approach is employed in the case of Dirichlet boundary conditions.
  • Self-adjoint curl operators
    Item type: Journal Article
    Hiptmair, Ralf; Kotiuga, Peter; Tordeux, Sébastien (2012)
    Annali di matematica pura ed applicata
  • Boundary regularity estimates for nonlocal elliptic equations in C1 and C1,α domains
    Item type: Journal Article
    Ros-Oton, Xavier; Serra, Joaquim (2017)
    Annali di matematica pura ed applicata
Publications 1 - 4 of 4