Results 51 to 56 of about 363 (56)

Uniform Lipschitz regularity of flat segregated interfaces in a singularly perturbed problem [PDF]

arXiv, 2015
For the singularly perturbed system \[\Delta u_{i,\beta}=\beta u_{i,\beta}\sum_{j\neq i}u_{j,\beta}^2, \quad 1\leq i\leq N,\] we prove that flat interfaces are uniformly Lipschitz. As a byproduct of the proof we also obtain the optimal lower bound near the flat interfaces, \[\sum_iu_{i,\beta}\geq c\beta^{-1/4}.\]
arxiv  

Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers. [PDF]

Entropy (Basel), 2020
Cherniha R, Davydovych V.
europepmc   +1 more source

Serrin's type overdetermined problems in convex cones [PDF]

arXiv, 2018
We consider overdetermined problems of Serrin's type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence of a solution implies that the domain is a spherical sector.
arxiv  

A Symmetry problem for some quasi-linear equations in Euclidean space [PDF]

arXiv
We prove sharp asymptotic estimates for the gradient of positive solutions to certain nonlinear $p$-Laplace equations in Euclidean space by showing symmetry and uniqueness of positive solutions to associated limiting problems.
arxiv  

A generalized radial integration by parts formula and its applications to Caffarelli-Kohn-Nirenberg inequalities. [PDF]

Anal Math Phys
Di Fratta G, Fiorenza A.
europepmc   +1 more source