250 papers
This paper generalizes the spacetime positive mass theorem to multiple time dimensions, proving that energy remains nonnegative and bounded by the trace norm of linear momenta, with equality implying a foliation by flat submanifolds and, under an umbilicity assumption, an isometric embedding into a generalized pp-wave.
This paper establishes the global well-posedness and uniform exponential stabilization of the critical quintic wave equation in a 3D bounded domain with locally distributed Kelvin-Voigt damping by combining frequency-space Littlewood-Paley analysis, critical Strichartz estimates, and microlocal defect measures to overcome derivative loss and geometric obstructions.
This paper constructs fractional Sobolev spaces with variable orders on arbitrary time scales and their product domains, establishing their functional-analytic properties and trace frameworks to derive Euler-Lagrange equations for variational problems involving variable-order Riemann-Liouville and Caputo fractional operators.
This paper establishes the detailed structure of oscillatory shock waves for the KdV-Burgers equation and proves their -contraction and uniform stability under arbitrarily large perturbations, thereby confirming the existence of zero viscosity-dispersion limits where Riemann shocks remain orbitally stable.
This paper establishes global well-posedness in the critical energy space and proves almost periodicity in time for the half-wave maps equation on the one-dimensional torus by leveraging its integrable Lax pair structure to derive explicit solution formulae and a general stability principle that extends to matrix-valued cases and companion results on the real line.
This paper establishes the quantitative stability of Kantorovich potentials and optimal transport maps on metric measure spaces with lower Ricci curvature bounds, confirming a recent conjecture by Kitagawa, Letrouit, and Mérigot through a novel proof using heat kernel-regularized -transforms that avoids reliance on linear structures or sectional curvature bounds.
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and initial displacement in a damped biharmonic wave equation by proving the forward problem's well-posedness via contraction semigroups and deriving explicit stability estimates that highlight the enhanced stability provided by the biharmonic structure and its dependence on the damping coefficient.
This paper investigates the conditions under which smooth maps are modulary dense on compact manifolds, specifically analyzing the validity and failure of this property in the context of the Lavrentiev gap.
This paper revisits the HED Method for Mullins-Sekerka evolution in the plane to establish not only the algebraic rate but also the sharp leading-order constant for convergence to a flat interface by introducing an intrinsic distance and deriving natural assumptions on the flow.
This paper investigates the Cauchy problem for a nonlinear damped Schrödinger equation involving the Riemann zeta function, establishing the uniqueness of distributional solutions, proving the existence of global solutions via regularization and compactness arguments, and demonstrating that solutions in the one-dimensional case vanish in finite time.
This paper establishes the existence, uniqueness, and global regularity of positive classical solutions to quasilinear Hamilton–Jacobi–Bellman equations on bounded convex domains via a constructive weighted monotone iteration scheme, while providing a probabilistic derivation from controlled Itô diffusions and demonstrating applications in stochastic production planning and image restoration.
This paper establishes the global Hölder continuity of solutions to the Dirichlet problem for the complex Monge-Ampère equation on strictly pseudoconvex domains or Hermitian manifolds, assuming the right-hand side belongs to and the boundary data are Hölder continuous.
This paper establishes a compactness result for the -convergence of integral functionals on -free vector fields to prove stochastic homogenization without periodicity assumptions, demonstrating that the homogenized integrand arises from limits of minimization problems on large cubes and can be explicitly characterized via the subadditive ergodic theorem under stochastic periodicity.
This paper establishes the local well-posedness of the generalized parabolic Anderson model and the -equation on the two-dimensional torus with random, noise-correlated coefficients by proving that naive renormalisation fails due to variance blow-up and instead demonstrating convergence through the use of random renormalisation functions supported by novel stochastic estimates.
This paper establishes the stability and uniqueness of a stochastic branching algorithm for solving semilinear heat equations by deriving sufficient criteria for the integrability of random functionals to prevent solution explosion.
This paper establishes the global-in-time existence of strong solutions for a class of fractional parabolic reaction-diffusion systems governed by spectral fractional Laplacians with polynomial growth nonlinearities, while also presenting numerical simulations to address an open theoretical question.
This paper establishes a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime by combining energy decay estimates with Sobolev embeddings to construct a bounded, locally Lipschitz scattering operator that maps past to future scattering data.
This paper establishes two weak formulations for the supercooled Stefan problem with transport noise, providing a probabilistic representation via a conditional McKean--Vlasov problem that characterizes finite-time blow-ups and continuous evolution based on initial conditions, while identifying a minimal solution that resolves instabilities through jump discontinuities.
This paper investigates heat equations with non-local Robin boundary conditions on bounded Lipschitz domains, demonstrating that while certain boundary operators can destroy the positivity-preserving property of the solution semigroup, the system still achieves ultracontractivity and exhibits eventual positivity under mild assumptions.
This paper establishes the convergence of the expected signature of a generalized physical Brownian motion to a nontrivial tensor in the small mass limit () by analyzing a graded PDE system, revealing that the limit differs from the standard mathematical Brownian motion and exhibits explicit combinatorial patterns when the system's coefficient matrix is diagonalizable.