Table of contents

CONTENTS Introduction Chapter I. General elliptic boundary-value problems § 1. The solubility of general elliptic boundary-value problems in domains with conic points § 2. The asymptotic behaviour of the solutions of a general boundary-value problem in the neighbourhood of a conic boundary point § 3. General boundary-value problems in non-smooth domains Chapter II. Boundary-value problems for the equations of mathematical physics in non-smooth domains § 1. Boundary-value problems for the system of elasticity theory § 2. Problems of hydrodynamics in domains with a non-smooth boundary § 3. The biharmonic equation Chapter III. Second-order elliptic equations in domains with a non-smooth boundary § 1. Boundary-value problems for second-order elliptic equations in an arbitrary domain § 2. Boundary-value problems in domains with isolated non-regular points on the boundary § 3. Second-order elliptic equations in domains with edges § 4. Boundary-value problems in domains that are diffeomorphic to a polyhedron Chapter IV. Parabolic and hyperbolic equations and systems in non-smooth domains § 1. Parabolic equations and systems in non-smooth domains § 2. Hyperbolic equations and systems in domains with singular points on the boundary References

CONTENTS Introduction Chapter I. Symplectic geometry § 1. Symplectic manifolds § 2. Submanifolds of a symplectic space § 3. Lagrangian manifolds, bundles, maps, and singularities Chapter II. Applications of the theory of Lagrangian singularities § 4. Oscillatory integral § 5. Integral points § 6. Metamorphoses of caustics Chapter III. Contact geometry § 7. Wave fronts § 8. Singularities of fronts § 9. Metamorphoses of fronts Chapter IV. The convolution of invariants and its generalizations § 10. Vector fields tangent to a front § 11. The linearized convolution of invariants § 12. Period maps and intersection forms Chapter V. Lagrangian and Legendrian topology § 13. Lagrangian and Legendrian cobordisms § 14. Lagrangian and Legendrian characteristic classes Chapter VI. Projections § 15. Singularities of projections of surfaces to a plane § 16. Singularities of projections of complete intersections § 17. The geometry of bifurcation diagrams References