Displaying similar documents to “Unique continuation for Schrödinger equations in dimensions three and four”

Unique continuation for elliptic equations and an abstract differential inequality

K. Senator (1994)

Studia Mathematica

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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 L p -norm. We prove that the zeros of the solutions are of at most finite order in the sense of a spherical L²-mean.

Sharp L p -weighted Sobolev inequalities

Carlos Pérez (1995)

Annales de l'institut Fourier

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We prove sharp weighted inequalities of the form ∫ R n | f ( x ) | p v ( x ) d x ≤ C ∫ R n | q ( D ) ( f ) ( x ) | p N ( v ) ( x ) d x where q ( D ) is a differential operator and N is a combination of maximal type operator related to q ( D ) and to p .

Unique continuation for |Δu| ≤ V |∇u| and related problems.

Thomas H. Wolff (1990)

Revista Matemática Iberoamericana

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Much of this paper will be concerned with the proof of the following Theorem 1. Suppose d ≥ 3, r = max {d, (3d - 4)/2}. If V ∈ Lloc r(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 Wloc 2,p and if |Δu|...

Unique continuation for Schrödinger operators with potential in Morrey spaces.

Alberto Ruiz, Luis Vega (1991)

Publicacions Matemàtiques

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Let us consider in a domain Ω of Rn solutions of the differential inequality |Δu(x)| ≤ V(x)|u(x)|, x ∈ Ω, where V is a non smooth, positive potential. We are interested in global unique continuation properties. That means that u must be identically zero on Ω if it vanishes on an open subset of Ω.

Mapping properties of integral averaging operators

H. Heinig, G. Sinnamon (1998)

Studia Mathematica

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Characterizations are obtained for those pairs of weight functions u and v for which the operators T f ( x ) = ʃ a ( x ) b ( x ) f ( t ) d t with a and b certain non-negative functions are bounded from L u p ( 0 , ∞ ) to L v q ( 0 , ∞ ) , 0 < p,q < ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.

A remark on Fefferman-Stein's inequalities.

Y. Rakotondratsimba (1998)

Collectanea Mathematica

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It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.