We study the minimal surface equation in Minkowskian geometry in R × R+, which is a well-known quasilinear wave equation. The classical result of Lindblad, [10] establishes global existence of small and smooth solutions (i.e. global regularity), provided the initial data is small, compactly supported and very smooth. In the present paper, we achieve more precise results. We show that, at least ...

Partial equilibrium analysis has a conceptual dilemma that its object should be negligibly small so as not to affect allocation of the other commodities but then the consumer does not care for it and the notion of willingness to pay for it does not make sense. In the setting of a continuum of commodities, we propose a limiting procedure which transforms the many-commodity environment into a par...

In this paper, we prove the global uniqueness of determining both the magnetic field and the electrical potential by boundary measurements in two-dimensional case. In other words, we prove the uniqueness of this inverse problem without any smallness assumption.

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

We study the non-linear Schödinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.

We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to must be harmonic if certain smallness and integrability conditions hold.