3 papers
math.AP2020
Optimal regularity for a two-phase obstacle-like problem with logarithmic singularity
Dennis Kriventsov, Henrik Shahgholian
We consider the semilinear problem \[ Δu = λ_+ \left(-\log u^+\right) 1_{\{u > 0\}} - λ_- \left(-\log u^- \right) 1_{\{u < 0\}} \qquad \hbox{ in } B_1, \] where is the unit b…
math.AP2017
Regularity for Shape Optimizers: The Degenerate Case
Dennis Kriventsov, Fanghua Lin
We consider minimizers of \[ F(λ_1(Ω),\ldots,λ_N(Ω)) + |Ω|, \] where is a function nondecreasing in each parameter, and is the -th Dirichlet eigenvalue of . This…
math.AP2015
Further time regularity for fully non-linear parabolic equations
Hector Chang-Lara, Dennis Kriventsov
We establish Hölder estimates for the time derivative of solutions of fully non-linear parabolic equations that does not necessarily have estimates.