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Creators/Authors contains: "Dong, Hongjie"

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  1. ; ; (, Mathematische Annalen)
    Free, publicly-accessible full text available May 1, 2026
  2. ; (, Advanced Nonlinear Studies)
    Abstract We present global Schauder type estimates in all variables and unique solvability results in kinetic Hölder spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations. The leading coefficients are Hölder continuous in thex,vvariables and are merely measurable in the temporal variable. Our proof is inspired by Campanato’s approach to Schauder estimates and does not rely on the estimates of the fundamental solution of the KFP operator. 
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    Free, publicly-accessible full text available March 12, 2026
  3. ; (, Calculus of Variations and Partial Differential Equations)
    Abstract We obtain new$$L_p$$ L p estimates for subsolutions to fully nonlinear equations. Based on our$$L_p$$ L p estimates, we further study several topics such as the third and fourth order derivative estimates for concave fully nonlinear equations, critical exponents of$$L_p$$ L p estimates and maximum principles, and the existence and uniqueness of solutions to fully nonlinear equations on the torus with free terms in the$$L_p$$ L p spaces or in the space of Radon measures. 
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  4. ; (, International Mathematics Research Notices)
    Abstract We study the global well-posedness of the supercritical dissipative surface quasi-geostrophic (SQG) equation, a key model in geophysical fluid dynamics. While local well-posedness is known, achieving global well-posedness for large initial data remains open. Motivated by enhanced decay in radial solutions, we aim to establish global well-posedness for small perturbations of potentially large radial data. Our main result shows that for small perturbations of radial data, the SQG equation admits a unique global solution. 
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    Free, publicly-accessible full text available November 22, 2025
  5. ; ; (, Calculus of Variations and Partial Differential Equations)
    Free, publicly-accessible full text available December 1, 2025
  6. ; ; (, Mathematische Annalen)
    Free, publicly-accessible full text available December 1, 2025
  7. ; ; ; (, SIAM Journal on Mathematical Analysis)
    Free, publicly-accessible full text available October 31, 2025
  8. ; (, SIAM Journal on Mathematical Analysis)
    Full Text Available 
  9. ; ; (, Transactions of the American Mathematical Society)
    In this paper, we consider higher regularity of a weak solution ( u , p ) (\mathbf {u},p) to stationary Stokes systems with variable coefficients. Under the assumptions that coefficients and data are piecewise C s , δ<#comment/> C^{s,\delta } in a bounded domain consisting of a finite number of subdomains with interfacial boundaries in C s + 1 , μ<#comment/> C^{s+1,\mu } , where s s is a positive integer, δ<#comment/> ∈<#comment/> ( 0 , 1 ) \delta \in (0,1) , and μ<#comment/> ∈<#comment/> ( 0 , 1 ] \mu \in (0,1] , we show that D u D\mathbf {u} and p p are piecewise C s , δ<#comment/> μ<#comment/> C^{s,\delta _{\mu }} , where δ<#comment/> μ<#comment/> = min { 1 2 , μ<#comment/> , δ<#comment/> } \delta _{\mu }=\min \big \{\frac {1}{2},\mu ,\delta \big \} . Our result is new even in the 2D case with piecewise constant coefficients. 
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    Full Text Available 
  10. ; ; (, The Journal of Geometric Analysis)
    Full Text Available