skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 2

Search for: All records

Award ID contains: 2044898

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, Bulletin of the London Mathematical Society)
    Abstract We consider rotated ‐Laplace systems on the unit ball of the formwhere , , and for some . We prove that with estimates. As a corollary, we obtain that solutions to , where is the Hardy space, have a higher integrability, namely, . 
    more » « less
    Free, publicly-accessible full text available November 1, 2025
  2. ; (, 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. 
    more » « less
    Full Text Available 
  3. ; ; ; (, Advances in Calculus of Variations)
    Abstract We extend the Calderón–Zygmund theory for nonlocal equations tostrongly coupled system of linear nonlocal equations ℒ A s ⁢ u = f {\mathcal{L}^{s}_{A}u=f}, where the operator ℒ A s {\mathcal{L}^{s}_{A}}is formally given by ℒ A s ⁢ u = ∫ ℝ n A ⁢ ( x , y ) | x - y | n + 2 ⁢ s ⁢ ( x - y ) ⊗ ( x - y ) | x - y | 2 ⁢ ( u ⁢ ( x ) - u ⁢ ( y ) ) ⁢ 𝑑 y . \mathcal{L}^{s}_{A}u=\int_{\mathbb{R}^{n}}\frac{A(x,y)}{|x-y|^{n+2s}}\frac{(x-%y)\otimes(x-y)}{|x-y|^{2}}(u(x)-u(y))\,dy. For 0 < s < 1 {0<1}and A : ℝ n × ℝ n → ℝ {A:\mathbb{R}^{n}\times\mathbb{R}^{n}\to\mathbb{R}}taken to be symmetric and serving asa variable coefficient for the operator, the system under consideration is the fractional version of the classical Navier–Lamé linearized elasticity system. The study of the coupled system of nonlocal equations is motivated by its appearance in nonlocal mechanics, primarily in peridynamics. Our regularity result states that if A ⁢ ( ⋅ , y ) {A(\,\cdot\,,y)}is uniformly Holder continuous and inf x ∈ ℝ n ⁡ A ⁢ ( x , x ) > 0 {\inf_{x\in\mathbb{R}^{n}}A(x,x)>0}, then for f ∈ L loc p {f\in L^{p}_{\rm loc}}, for p ≥ 2 {p\geq 2}, the solution vector u ∈ H loc 2 ⁢ s - δ , p {u\in H^{2s-\delta,p}_{\rm loc}}for some δ ∈ ( 0 , s ) {\delta\in(0,s)}. 
    more » « less
    Free, publicly-accessible full text available November 17, 2025
  4. ; ; ; (, Journal of the European Mathematical Society)
    We investigate minimizers and critical points for scale-invariant tangent-point energies{\mathrm{TP}}^{p,q}of closed curves. We show that (a) minimizing sequences in ambient isotopy classes converge to locally critical embeddings at all but finitely many points and (b) locally critical embeddings are regular. Technically, the convergence theory (a) is based on a gap estimate for fractional Sobolev spaces with respect to the tangent-point energy. The regularity theory (b) is based on constructing a new energy\mathcal{E}^{p,q}and proving that the derivative\gamma'of a parametrization of a{\mathrm{TP}}^{p,q}-critical curve\gammainduces a critical map with respect to\mathcal{E}^{p,q}acting on torus-to-sphere maps. 
    more » « less
    Free, publicly-accessible full text available April 9, 2026
  5. ; ; (, Memoirs of the American Mathematical Society)
    We consider minimizing harmonic maps u u from Ω<#comment/> ⊂<#comment/> R n \Omega \subset \mathbb {R}^n into a closed Riemannian manifold N \mathcal {N} and prove: 1. an extension to n ≥<#comment/> 4 n \geq 4 of Almgren and Lieb’s linear law. That is, if the fundamental group of the target manifold N \mathcal {N} is finite, we have\[ H n −<#comment/> 3 ( sing ⁡<#comment/> u ) ≤<#comment/> C ∫<#comment/> ∂<#comment/> Ω<#comment/> | ∇<#comment/> T u | n −<#comment/> 1 d H n −<#comment/> 1 ; \mathcal {H}^{n-3}(\operatorname {sing} u) \le C \int _{\partial \Omega } |\nabla _T u|^{n-1} \,\mathrm {d}\mathcal {H}^{n-1}; \]2. an extension of Hardt and Lin’s stability theorem. Namely, assuming that the target manifold is N = S 2 \mathcal {N}=\mathbb {S}^2 we obtain that the singular set of u u is stable under small W 1 , n −<#comment/> 1 W^{1,n-1} -perturbations of the boundary data. In dimension n = 3 n=3 both results are shown to hold with weaker hypotheses, i.e., only assuming that the trace of our map lies in the fractional space W s , p W^{s,p} with s ∈<#comment/> ( 1 2 , 1 ] s \in (\frac {1}{2},1] and p ∈<#comment/> [ 2 , ∞<#comment/> ) p \in [2,\infty ) satisfying s p ≥<#comment/> 2 sp \geq 2 . We also discuss sharpness. 
    more » « less
    Full Text Available 
  6. ; ; ; (, SIAM Journal on Mathematical Analysis)
    Full Text Available 
  7. ; ; (, 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 dimension d ≥<#comment/> 3 d \geq 3 in the natural energy class. 
    more » « less
  8. ; ; (, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)
    Full Text Available 
  9. ; (, Nonlinear Analysis)
    Full Text Available 
  10. ; (, Mathematische Annalen)
    Full Text Available