Results 71 to 80 of about 394,604 (313)
Communications on Pure and Applied Mathematics, Volume 78, Issue 3, Page 545-591, March 2025.Abstract While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time‐dependent ...
Dennis Kriventsov, Georg S. Weiss
wiley +1 more source
Renormalized solutions of semilinear elliptic equations with general measure data [PDF]
Monatshefte für Mathematik (Print), 2016 In the paper we first propose a definition of renormalized solution of semilinear elliptic equation involving operator corresponding to a general (possibly nonlocal) symmetric regular Dirichlet form satisfying the so-called absolute continuity condition ...
Tomasz Klimsiak, A. Rozkosz
semanticscholar +1 more source
Unique continuation property and local asymptotics of solutions to fractional elliptic equations [PDF]
, 2013 Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up arguments, we describe the exact behavior near the ...
Fall, Mouhamed Moustapha, Veronica Felli
core
A nonlinear characterization of stochastic completeness of graphs
Mathematische Nachrichten, Volume 298, Issue 3, Page 925-943, March 2025.Abstract We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem.
Marcel Schmidt, Ian Zimmermann
wiley +1 more source
Reduced measures for semilinear elliptic equations involving Dirichlet operators [PDF]
, 2016 We consider elliptic equations of the form (E) $$-Au=f(x,u)+\mu $$-Au=f(x,u)+μ, where A is a negative definite self-adjoint Dirichlet operator, f is a function which is continuous and nonincreasing with respect to u and $$\mu $$μ is a Borel measure of ...
Tomasz Klimsiak
semanticscholar +1 more source
, 2011 The asymptotic behavior of solutions to Schr\"odinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the singularity of ...
Felli, Veronica +2 more
core +1 more source
On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates
Communications on Pure and Applied Mathematics, Volume 78, Issue 2, Page 211-322, February 2025.Abstract Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation
Yu Deng +2 more
wiley +1 more source
Hermite solution for a new fractional inverse differential problem
Mathematical Methods in the Applied Sciences, Volume 48, Issue 3, Page 3811-3824, February 2025.Mathematics, mathematical modeling of real systems, and mathematical and computer methodologies aimed at the qualitative and quantitative study of real physical systems interact in a nontrivial way. This work aims to examine a new class of inverse problems for a fractional partial differential equation with order fractional 0<ρ≤1$$ 0<\rho \le 1 ...
Mohammed Elamine Beroudj +2 more
wiley +1 more source
Electronic Journal of Differential Equations, 2000 solutions to nonlinear equations and to (non)resonant semilinear equations involving nonlinear perturbations of Fredholm maps of index zero. We apply our results to semilinear elliptic, and to semilinear parabolic and hyperbolic periodic boundary-value ...
P. S. Milojevic
doaj
Multiple solutions for a class of semilinear elliptic equations [PDF]
arXiv, 2020 By using truncation technique, minimization method and Morse theory, we obtain three nontrivial solutions for a class of semilinear elliptic equations.
arxiv