Interior Regularity Results

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Related lectures (31)

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Lecture 4: Hilbert Spaces and Unique Solutions

Covers Hilbert spaces and unique solutions in function spaces, emphasizing the Lax-Milgram theorem.

Scalar Products: Definition, Examples

Covers the definition of a scalar product on a real vector space and provides examples.

Completeness of Lp Spaces

Delves into the completeness of Lp spaces and the density of function classes in L².

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Embedding in Function Spaces

Explores embedding in function spaces, including elliptic equations, Hölder inequality, Lorentz space, and Hardy-Young inequality.

Function Spaces and Hilbert Spaces

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Properties of Weak Derivatives

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Polyconvexity

Explores polyconvexity in vectorial calculus with open bounded sets and Lipschitz boundaries, weak continuity theorems, and function space minimization.

Interpolation in Finite Element Spaces

Covers interpolation in finite element spaces and the regularity of solutions in convex domains.