Lecture

Abstract Variational Problems

Related lectures (31)

Lax-Milgram: Variational Problems and Riesz's Theorem

Explores the Lax-Milgram theorem, variational problems, and Riesz's representation theorem in linear elliptic problems.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Bilinear Forms: Theory and Applications

Covers the theory and applications of bilinear forms in various mathematical contexts.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Weingarten Application of Regular Surfaces

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Quantization: Topological Operators

Covers the quantization of topological operators and Ising models on square lattices.

Interpolation of Lagrange: Dualité and Coupling

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Finite Element Method: Weak Solutions

Covers weak solutions in the finite element method, emphasizing continuity and the Cauchy-Schwarz inequality.

Signal Representations

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Principles of Quantum Physics

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Hilbert Space: State, Evolution, Measurement

Introduces Hilbert space as a big place where quantum systems evolve with unitaries.

Geometric Properties of Dot Product

Covers the geometric properties of the dot product and its algebraic aspects.