2 citations · 2 across the 3 of their papers we have counts for
5 papers
One-phase free boundary solutions of finite Morse index
José Basulto, Nikola Kamburov
We study global solutions to the classical one-phase free boundary problem that have finite Morse index relative to the Alt-Caffarelli functional. We show that such solutions are s…
Uniform a priori estimates for positive solutions of the Lane-Emden system in the plane
Nikola Kamburov, Boyan Sirakov
We prove that positive solutions of the superlinear Lane-Emden system in a two-dimensional smooth bounded domain are bounded independently of the exponents in the system, provided…
Nontrivial solutions to Serrin's problem in annular domains
Nikola Kamburov, Luciano Sciaraffia
We construct nontrivial smooth bounded domains of the form , bifurcating from annuli, for which there exists a positive soluti…
Free boundaries subject to topological constraints
David S. Jerison, Nikola Kamburov
We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamen…
Uniform a priori estimates for positive solutions of the Lane-Emden equation in the plane
Nikola Kamburov, Boyan Sirakov
We prove that positive solutions of the Lane-Emden equation in a two-dimensional smooth bounded domain are uniformly bounded for all large exponents.