2 citations · 2 across the 7 of their papers we have counts for
10 papers
Nontrivial periodic solutions to the one-phase free boundary problem
José Basulto, Nikola Kamburov
We construct new classical global solutions of the one-phase Bernoulli free boundary problem in whose positive phases are periodic perturbations of the product of th…
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…
Nondegeneracy and stability in the limit of a one-phase singular perturbation problem
Nikola Kamburov
We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We in…
Nondegeneracy for stable solutions to the one-phase free boundary problem
Nikola Kamburov, Kelei Wang
We prove the nondegeneracy condition for stable solutions to the one-phase free boundary problem. The proof is by a De Giorgi iteration, where we need the Sobolev inequality of Mic…
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.
Structure of one-phase free boundaries in the plane
David Jerison, Nikola Kamburov
We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connect…
A free boundary problem inspired by a conjecture of De Giorgi
Nikola Kamburov
We study global monotone solutions of the free boundary problem that arises from minimizing the energy functional , where is the characteris…