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We will present a unique continuation result for solutions of second order differential equations of real principal type with critical potential in (where is the number of variables) across non-characteristic pseudo-convex hypersurfaces. To obtain unique continuation we prove Carleman estimates, this is achieved by constructing a parametrix for the operator conjugated by the Carleman exponential weight and investigating its boundedness properties.
In this article we discuss some estimates of the number of the negative eigenvalues and their moments of energy for an elliptic operator L = L0 - V(x) defined in Hm(R+n) with the Robin boundary conditions containing a potential W(x), in terms of some integrals of V and W.
We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.
We study the stabilization of global solutions of the
Kawahara (K) equation in a bounded interval, under the effect of
a localized damping mechanism. The Kawahara equation is a model
for small amplitude long waves. Using multiplier techniques and
compactness arguments we prove the
exponential decay of the solutions of the (K) model. The proof
requires of a unique continuation theorem and the smoothing effect
of the (K) equation on the real line, which are proved in this work.
This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients λ, µin three dimensions, whereλ and μ are Lipschitz continuous and V∈L∞. The method is based on the Carleman estimate with polynomial weights for the Lamé operator.
This paper studies the strong unique continuation property for the
Lamé system of elasticity with variable Lamé coefficients
λ, µ in three dimensions,
where λ and μ are Lipschitz continuous and V∈L∞. The method is based on the Carleman estimate with polynomial weights for the Lamé operator.
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