Displaying similar documents to “Jacobi fields and regularity of functions of least gradient”

On the maximum modulus theorem for nonanalytic functions in several complex variables.

Mario O. González Rodríguez (1981)

Revista Matemática Hispanoamericana

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Let w = f(z, ..., z) = u(x, ..., y) + iv(x, ..., y) be a complex function of the n complex variables z, ..., z, defined in some open set A ⊂ C. The purpose of this note is to prove a maximum modulus theorem for a class of these functions, assuming neither the continuity of the first partial derivatives of u and v with respect to x and y, nor the conditions f = 0 in A for k = 1, 2, ..., n (the Cauchy-Riemann equations in complex form).

A comparison theorem for the Levi equation

Giovanna Citti (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove a strong comparison principle for the solution of the Levi equation L ( u ) = ∑ i = 1 n ( ( 1 + u t 2 ) ( u x i ⁢ x i + u y i ⁢ y i ) + ( u x i 2 + u y i 2 ) u t ⁢ t + 2 ( u y i - u x i u t ) u x i ⁢ t - 2 ( u x i + u y i u t ) u y i ⁢ t + k ( x , y , t ) ( 1 + | D u | 2 ) 3 / 2 = 0 , applying Bony Propagation Principle.