Objective
The objective of the project is the study of spectral properties of elliptic, especially two-term, asymptotic formulae for the counting function, the study of the negative spectrum of the Schrödinger operator and its generalizations, the spectral theory of Sturm-Liouville equations with non-decaying potentials, the spectral theory of Douglis-Nirenberg type elliptic systems, spectral theory of degenerate elliptic equations and the spectral theory of elliptic operators in domains with irregular (in particular, fractal) boundaries.
The necessary technical tools will also be developed, such as the theory of branching Hamiltonian billiards, the theory of global oscillatory integrals with complex phase functions, Tauberian theorems, qualitative and quantitative properties of function spaces and the theory of pseudo-differential operators. Elliptic systems arising in continuum mechanics, non-linear evolution problems and completely integrable systems will also be considered. A detailed analysis of the behaviour of solutions of elliptic and parabolic differential equations in domains with conical and angular points will be carried out.
Topic(s)
Call for proposal
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BN1 9QH BRIGHTON / FALMER
United Kingdom