Energy concentration for the Landau–Lifshitz equation

Energy solutions and concentration problem of fractional Schrödinger equation

Energy concentration and Sommerfeld condition for Helmholtz equation with variable index at infinity

We consider the Helmholtz equation with a variable index of refraction n(x), which is not necessarily constant at infinity but can have an angular dependency like n(x) → n ∞ (x/|x|) as |x| → ∞. Under some appropriate assumptions on this convergence and on n ∞ we prove that the Sommerfeld condition at infinity still holds true under the explicit form R d ∇u − in 1/2 ∞ u x |x| 2 dx |x| < +∞. It i...

Energy Bounds for the Spinless Salpeter Equation

We study the spectrum of the Salpeter Hamiltonian H = β √ m2 + p2 +V (r), where V (r) is an attractive central potential in three dimensions. If V (r) is a convex transformation of the Coulomb potential −1/r and a concave transformation of the harmonic-oscillator potential r, then upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form ...

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

Concentration Compactness for the Critical Maxwell-klein-gordon Equation

We prove global regularity, scattering and a priori bounds for the energy critical MaxwellKlein-Gordon equation relative to the Coulomb gauge on (1 + 4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gérard profile decomposition [1] and a concentration compactness/rigidity argument by Kenig-Merle [5], following the method developed by the first author and Schlag [10] in...