Kernel Functions and Elliptic Differential Equations in Mathematical Physics

By S. Bergman, M. Schiffer. 2005

170 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c04f374c7665ad24d7d6cbe8852ca78db26ac51e

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In Computational Theory and Mathematics

Citations in the corpus

On Two Approaches to the Bergman Theory for Slice Regular Functions (2013, background): “The literature is very wide and as classical reference books, in the case of holomorphic functions, we mention [1, 2, 19].”
Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, background): “We call it the Bergman kernel after the work of Korotkin and Kokotov [34], and also because Bergman together with Schiffer are the main contributors to its study [7].”
The C-property for slice regular functions and applications to the Bergman space (2013, background): “We finally mention the classical references for the Bergman theory in the complex case [1, 2] and for the sake of completeness some papers that treat the Bergman theory in the hypercomplex setting [3, 4, 11, 12, 13, 14, 17, 19, 20, 21].”
A posteriori error estimates for the Steklov eigenvalue problem (2008, background): “Some of these spectral problems lead to a Steklov eigenvalue problem similar to the one considered here, for instance, in the study of surface waves [7], in the analysis of stability of mechanical oscillators immersed in a viscous fluid ([12] and the references therein) and in the study of the vibra”
Nonconforming finite element approximations of the Steklov eigenvalue problem (2009, background): “For instance, they are found in the study of surface waves (see [8]), in the analysis of stability of mechanical oscillators immersed in a viscous fluid (see [14] and the references therein), in the study of the vibration modes of a structure in contact with an incompressible fluid (see, for example”
Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations (2013, background): “We know from [9] and [12] that the eigenvalue problem (1.”
A general boundary value problem and its Weyl function (2007, background): “The classical approach of boundary value problems theory (see [ 4 , 28] for instance) considers two semihomogeneous problems obtained from (3.1) by putting f = 0, ' 6= 0 and f 6= 0, ' = 0. The solution to (3.1) then is sought in the form of sum of solutions to these auxiliary problems.”
Invariants of algebraic curves and topological expansion (2007, background): “• For κ = (τ − τ), B is the Schiffer kernel [10, 48], and it is modular invariant.”
Steklov Eigenproblems and the Representation of Solutions of Elliptic Boundary Value Problems (2005, methodology): “The solution operators classically have been defined using Poisson, Robin or Neumann boundary integral kernels as in part B of Bergman and Schiffer ( 1953 ).”