Differential and Integral Equations

Parameter-elliptic boundary value problems connected with the Newton polygon

Robert Denk and Leonid Volevich

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In this paper pencils of partial differential operators depending polynomially on a complex parameter and corresponding boundary value problems with general boundary conditions are studied. We define a concept of ellipticity for such problems (for which the parameter-dependent symbol in general is not quasi-homogeneous) in terms of the Newton polygon and introduce related parameter-dependent norms. It is shown that this type of ellipticity leads to unique solvability of the boundary value problem and to two-sided a priori estimates for the solution.

Article information

Differential Integral Equations, Volume 15, Number 3 (2002), 289-326.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J40: Boundary value problems for higher-order elliptic equations
Secondary: 46N20: Applications to differential and integral equations 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)


Denk, Robert; Volevich, Leonid. Parameter-elliptic boundary value problems connected with the Newton polygon. Differential Integral Equations 15 (2002), no. 3, 289--326. https://projecteuclid.org/euclid.die/1356060862

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