Carleman Inequalities for the Dirac Operator and Strong Unique Continuation

Carleman Inequalities and the Heat Operator

1. Introduction. The unique continuation property is best understood for second-order elliptic operators. The classic paper by Carleman [8] established the strong unique continuation theorem for second-order elliptic operators that need not have analytic coefficients. The powerful technique he used, the so-called " Carleman weighted inequality, " has played a central role in later developments....

Unique Continuation Theorems for the ∂̄-operator and Applications

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary point z0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away from z0 cannot vanish to infinite order at z0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the...

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients

In this work we obtain strong unique continuation results for variable coefficient second order parabolic equations. The coefficients in the principal part are assumed to satisfy a Lipschitz condition in x and a Hölder C 1 3 condition in time. The coefficients in the lower order terms, i.e. the potential and the gradient potential, are allowed to be unbounded and required only to satisfy mixed ...

Carleman estimates and unique continuation for second order elliptic equations with nonsmooth coefficients