arXiv subjects

Sebastián Flores Sepúlveda

Publications and source records attributed to Sebastián Flores Sepúlveda.

2 recordsLinked to original sources

arXiv2026

The Landis Conjecture For Nonlocal Elliptic Operators: Polynomial Decay

We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption $o(|x|^{-(N+2s)})$ at infinity. Our result is new even in the case of the fractional Laplacian, as it unveils the nonlocal nature of the decay in Landis conjecture, evolving from exponential to polynomial.

math.AP↗

arXiv2026

On the shape of the positivity region for a free boundary problem describing cell polarization

In this paper we study a mass-constrained free boundary problem modeling cell polarization, in the regime where the mass is small. In the generic case of a signal with nondegenerate maxima, we prove that the solution converges locally to a global, integrable solution to an obstacle problem in the plane. We further show that the interface of the solution to the limit problem is an ellipse, the equation of which is explicit. We also study some cases where the signal has degenerate maxima, highlighting a variety of possible behaviors.

math.AP↗