253 papers
This paper establishes sharp rates of propagation of chaos for McKean-Vlasov equations with non-linear measure-dependent coefficients, applying these results to derive uniform-in-time convergence guarantees for mean field Langevin dynamics, control, and games by combining the BBGKY hierarchy with weak propagation techniques.
This paper establishes nontangential maximal function estimates for the gradient of solutions to elliptic operators with variable, bounded, measurable coefficients on Lipschitz domains, addressing a mixed boundary value problem with Neumann and Dirichlet-regularity data that generalizes both pure boundary problems and the classical Laplacian case.
This paper establishes uniform Hölder bounds and analyzes the strong competition limit of variational reaction-diffusion systems driven by -wise interactions (), proving that minimizers converge to partially segregated configurations that satisfy specific regularity and extremality conditions.
This paper establishes the sharp finite-time Type-I blowup for the three-dimensional incompressible Euler equations in the axisymmetric no-swirl class with initial velocity in for every , utilizing a novel Lagrangian framework to prove that the quadratic strain term dominates the pressure Hessian uniformly below the critical regularity threshold of .
This paper investigates the long-time dynamics of a bulk-surface convective Cahn--Hilliard system by establishing instantaneous regularization, proving the existence of a minimal pullback attractor for the resulting non-autonomous system, and demonstrating convergence to a single steady state under decay assumptions on the velocity fields using the Łojasiewicz–Simon inequality.
This paper introduces the concept of F-convexity as a generalization of power convexity and characterizes which specific F-convexities are preserved under both the standard heat flow in Euclidean space and the Dirichlet heat flow in convex domains.
This paper establishes the global well-posedness and constructs self-similar solutions for a semilinear elliptic equation with a nonlinear dynamic boundary condition in the half-space by utilizing the broader framework of Morrey spaces to accommodate rough, non-decaying initial data and deriving key estimates for associated interior and boundary operators.
This paper introduces the concept of strong regularity for subanalytic sheaves to establish microsupport estimates and derive initial value and division theorems for multi-microlocal objects, ultimately yielding a multi-microlocal version of Bochner's tube theorem for solutions of regular D-modules.
This paper establishes sharper polyhomogeneous mapping properties for the Radon transform and backprojection operator on the unit ball by constructing a double -fibration to desingularize the point-hyperplane relation and utilizing associated -fibration operations to improve upon classic Mellin-based estimates.
This paper establishes the existence and Liouville-type results for quadratic growth solutions to fully nonlinear elliptic equations with periodic coefficients and right-hand sides, proving that under a small oscillation assumption, such solutions decompose into the sum of a quadratic polynomial and a periodic function.
This paper investigates the asymptotic behavior of solutions to divergence-form linear elliptic equations in exterior domains with periodic coefficients, thereby generalizing the Liouville-type result originally established by Avellaneda and Lin.
This paper establishes that for eigenfunctions of complex constant-coefficient elliptic operators, either the inner radius of the nonvanishing set scales as or the entire mass concentrates in a boundary layer of the same width as the eigenvalue magnitude grows.
This paper proves that for the fractional Laplacian with nonlocal Neumann boundary conditions in an -dimensional ball, the eigenspace corresponding to the first nontrivial eigenvalue is generated by antisymmetric eigenfunctions with exactly two nodal domains when the fractional order is sufficiently close to 1.
This paper investigates a mathematical model of bacterial biofilms in a continuously stirred tank reactor with wall attachment, establishing global well-posedness and analyzing the stability and existence of both trivial and nontrivial equilibrium states.
This paper proves that the potential function of a complete Kähler-Einstein metric on a bounded strictly convex domain in is itself strictly convex.
This paper investigates the near-field refraction problem in negative refractive index materials with energy loss by analyzing two distinct relative refractive index regimes, defining the refractor, examining Fresnel coefficients, and proving the existence of weak solutions for discrete or finite Radon target measures, while also briefly addressing the critical case where the index equals -1.
This paper establishes the well-posedness and regularity of a class of degenerate hyperbolic equations with a boundary degeneracy, introduces a shape-design approximation via domain regularization to prove solution convergence, and derives an observability inequality for the original degenerate system by leveraging uniform observability results from the regularized problems.
This paper provides an elementary proof, inspired by Korevaar and Schoen, of the local Lipschitz regularity for suitable weak solutions of the heat flow of harmonic maps from a complete Riemannian manifold with positive injectivity radius and bounded curvature into any CAT(0)-metric space.
Under extremely mild growth assumptions, this paper classifies the solutions of a mixed-order conformally invariant system in and featuring exponential and nonlocal nonlinearities, a system closely related to extensively studied conformally invariant equations.
This paper establishes the existence of piecewise smooth self-similar solutions for the supersonic flow of a Chaplygin gas over a conical wing with -shaped cross sections by reformulating the problem as a boundary value problem for a nonlinear mixed-type equation and applying the continuity method, thereby verifying part of Küchemann's speculation and identifying a new conical flow field structure.