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A pure smoothness condition for Radó’s theorem for α -analytic functions

Abtin Daghighi, Frank Wikström (2016)

Czechoslovak Mathematical Journal

Let Ω n be a bounded, simply connected -convex domain. Let α + n and let f be a function on Ω which is separately C 2 α j - 1 -smooth with respect to z j (by which we mean jointly C 2 α j - 1 -smooth with respect to Re z j , Im z j ). If f is α -analytic on Ω f - 1 ( 0 ) , then f is α -analytic on Ω . The result is well-known for the case α i = 1 , 1 i n , even when f a priori is only known to be continuous.

An approach based on matrix polynomials for linear systems of partial differential equations

N. Shayanfar, M. Hadizadeh (2013)

Special Matrices

In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method...

Dispersive estimates and absence of embedded eigenvalues

Herbert Koch, Daniel Tataru (2005)

Journées Équations aux dérivées partielles

In [2] Kenig, Ruiz and Sogge proved u L 2 n n - 2 ( n ) L u L 2 n n + 2 ( n ) provided n 3 , u C 0 ( n ) and L is a second order operator with constant coefficients such that the second order coefficients are real and nonsingular. As a consequence of [3] we state local versions of this inequality for operators with C 2 coefficients. In this paper we show how to apply these local versions to the absence of embedded eigenvalues for potentials in L n + 1 2 and variants thereof.

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