Notably, advances in establishing Hessian estimates for Lagrangian mean curvature equations have yielded sharper regularity results by rigorously bounding second-order derivatives.

DNS particle trajectories in the Lagrangian Cloud. η is the Kolmogorov length and τη is the Kolmogorov time. Credit: Physical Review Research (2025). DOI: 10.1103/PhysRevResearch.7.023225 A sneeze.

The authors' optimization procedures stem from Lagrangian methods for approaching nonlinear problems, and demonstrate an efficient, exact means of calculating the shape derivative of the cost ...

Higher-Derivative Field Theories: Theories in which the Lagrangian or action includes derivatives of the fields higher than the first order, leading to additional degrees of freedom and novel ...

Point interactions for the n-th derivative operator in one dimension are investigated. Every such perturbed operator coincides with a selfadjoint extension of the n-th derivative operator restricted ...