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math.AP2026
Sharp gradient bounds for uniformly elliptic PDE, eigenvalue asymptotics, and the Landis conjecture
Boyan Sirakov, Philippe Souplet
We study three classical problems in the theory of linear second-order uniformly elliptic equations: (i) gradient estimates for the Dirichlet problem, (ii) estimates and asymptotic…
math.AP2026
Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form
Philippe Souplet, Boyan Sirakov
This paper presents two types of novel, qualitative and quantitative, estimates for positive solutions of general uniformly elliptic PDEs in divergence form. First, we prove a More…
math.AP2026
A priori estimates and exact solvability for non-coercive stochastic control equations
Maria Luísa Pasinato, Boyan Sirakov
We establish, for the first time, explicit a priori and regularity estimates for solutions of the Dirichlet problem for Hamilton-Jacobi-Bellman operators from stochastic control, w…