Differential and Integral Equations
- Differential Integral Equations
- Volume 15, Number 3 (2002), 289-326.
Parameter-elliptic boundary value problems connected with the Newton polygon
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.
Differential Integral Equations, Volume 15, Number 3 (2002), 289-326.
First available in Project Euclid: 21 December 2012
Permanent link to this document
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