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L p -inequalities for the laplacian and unique continuation

W. O. Amrein, A. M. Berthier, V. Georgescu (1981)

Annales de l'institut Fourier

We prove an inequality of the type | x | r f L p ( R n ) c ( n , p , q , r ) | x | τ + μ Δ f L q ( R n ) . This is then used to derive the unique continuation property for the differential inequality | Δ f ( x ) | | v ( x ) | | f ( x ) | under suitable local integrability assumptions on the function v .

L p - L q -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki (1991)

Annales Polonici Mathematici

We prove the L p - L q -time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the L p - L q -time decay estimates.

L1 and L∞-estimates with a local weight for the ∂-equation on convex domains in Cn.

Francesc Tugores (1992)

Publicacions Matemàtiques

We construct a defining function for a convex domain in Cn that we use to prove that the solution-operator of Henkin-Romanov for the ∂-equation is bounded in L1 and L∞-norms with a weight that reflects not only how near the point is to the boundary of the domain but also how convex the domain is near the point. We refine and localize the weights that Polking uses in [Po] for the same type of domains because they depend only on the Euclidean distance to the boudary and don't take into account the...

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