Towards the Cauchy problem for the Laplace equation
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.
Über die Differentialgleichung rt - s2 = f und das Weylsche Einbettungsproblem.
Über Differentialgleichungen der From F(z, ...)w... - n(n +1)w = 0.
Über nichtlineare, konkave, elliptische Differentialgleichungen.
Unicité forte à partir d'une variété de dimension quelconque pour des inégalités différentielles elliptiques
Uniform bounds for quotients of Green functions on -domains
Let , be elliptic operators with Hölder continuous coefficients on a bounded domain of class . There is a constant depending only on the Hölder norms of the coefficients of and its constant of ellipticity such thatwhere (resp. ) are the Green functions of (resp. ) on .
Uniformly Elliptic PDEs with Bounded, Measurable Coefficients.
Unique continuation for elliptic equations and an abstract differential inequality
We consider a class of elliptic equations whose leading part is the Laplacian and for which the singularities of the coefficients of lower order terms are described by a mixed -norm. We prove that the zeros of the solutions are of at most finite order in the sense of a spherical L²-mean.
Unique continuation for |Δu| ≤ V |∇u| and related problems.
Much of this paper will be concerned with the proof of the followingTheorem 1. Suppose d ≥ 3, r = max {d, (3d - 4)/2}. If V ∈ Llocr(Rd), then the differential inequality |Δu| ≤ V |∇u| has the strong unique continuation property in the following sense: If u belongs to the Sobolev space Wloc2,p and if |Δu| ≤ V |∇u| andlimR→0 R-N ∫|x| < R |∇u|p' = 0for all N then u is constant.
Unique continuation with weak type lower order terms: The variable coefficient case.
This paper deals with the unique continuation problems for variable coefficient elliptic differential equations of second order. We will prove that the unique continuation property holds when the variable coefficients of the leading term are Lipschitz continuous and the coefficients of the lower order terms have small weak type Lorentz norms. This will improve an earlier result of T. Wolff in this direction.
Uniqueness for first-order hyperbolic systems - with applications to secnd-order elliptic third-order and Maxwell's equations.
Using stochastic comparison to estimate Green's functions
estimates for solutions to non-uniformly elliptic PDE'S with measurable coefficients.
Weak Bloch property and weight estimates for elliptic operators
Weak discrete maximum principles
We introduce weak discrete maximum principles for matrix equations associated with some elliptic problems. We also give an example on discrete maximum principles.
Zur Konstruktion gewisser Integraloperatoren für partielle Differentialgleichungen Teil II.
Zur Konstruktion gewisser Integraloperatoren für partielle Differentialgleichungen Teil I.
Априорные оценки для решений нелинейных эллиптических уравнений второго порядка
Асимптотики фундаментальных решений дивергентных дифференциальных уравнений второго порядка