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Creators/Authors contains: "Schikorra, Armin"

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  1. ; ; ; ( , SIAM Journal on Mathematical Analysis)
    Free, publicly-accessible full text available April 30, 2025
  2. ; ; ( , Transactions of the American Mathematical Society, Series B)

    Extending an argument by Shatah and Struwe [Int. Math. Res. Not. 11 (2002), pp. 555–571] we obtain uniqueness for solutions of the half-wave map equation in dimensiond≄<#comment/>3d \geq 3in the natural energy class.

     
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  3. ; ( , Nonlinear Analysis)
    Free, publicly-accessible full text available October 1, 2024
  4. ; ( , Mathematische Annalen)
    Free, publicly-accessible full text available September 30, 2024
  5. ; ( , Journal of the London Mathematical Society)
    Abstract

    Let a closed ‐dimensional manifold, be a closed manifold, and let for . We extend the monumental work of Sacks and Uhlenbeck by proving that if , then there exists a minimizing ‐harmonic map homotopic to . If , then we prove that there exists a ‐harmonic map from to in a generating set of . Since several techniques, especially Pohozaev‐type arguments, are unknown in the fractional framework (in particular, when , one cannot argue via an extension method), we develop crucial new tools that are interesting on their own: such as a removability result for point singularities and a balanced energy estimate for nonscaling invariant energies. Moreover, we prove the regularity theory for minimizing ‐maps into manifolds.

     
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    Free, publicly-accessible full text available August 1, 2024
  6. ; ; ( , Calculus of Variations and Partial Differential Equations)
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  7. ; ( , Studia Mathematica)
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  8. ; ( , Ball State undergraduate mathematics exchange)
    Accepted Manuscript Full Text Available
  9. ; ; ( , IMA Journal of Numerical Analysis)
    Abstract This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet energy on unit-length vector fields. We devise and analyze numerical methods for the approximation of various partial differential equations related to fractional harmonic maps. The compactness results imply the convergence of numerical approximations. Numerical examples on spin chain dynamics and point defects are presented to demonstrate the effectiveness of the proposed methods. 
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  10. ; ; ; ( , Partial Differential Equations and Applications)
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