TY  - BOOK
AU  - 
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains 
T2  - Lecture Notes in Mathematics,
SN  - 9783642122453
AV  - QA1-939 
U1  - 510 23
PY  - 2010///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Functional analysis
KW  - Global differential geometry
KW  - Materials
KW  - Mathematics, general
KW  - Functional Analysis
KW  - Differential Geometry
KW  - Continuum Mechanics and Mechanics of Materials
N1  - Models of Higher Order -- Linear Problems -- Eigenvalue Problems -- Kernel Estimates -- Positivity and Lower Order Perturbations -- Dominance of Positivity in Linear Equations -- Semilinear Problems -- Willmore Surfaces of Revolution; ZDB-2-SMA; ZDB-2-LNM
N2  - This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on ǣnear positivity.ǥ The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the rst part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenberg-type symmetry result is included. Finally, some recent progress on the Dirichlet problem for Willmore surfaces under symmetry assumptions is discussed
UR  - http://dx.doi.org/10.1007/978-3-642-12245-3
ER  -