MATH-305: Introduction to partial differential equations

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Lectures in this course (53)

Lax-Milgram: Variational Problems and Riesz's Theorem

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

Abstract Variational Problems

Covers abstract variational problems in Hilbert spaces, focusing on boundedness, continuity, and coercivity.

Well-Posedness of Elliptic PDEs

Explores the well-posedness of elliptic partial differential equations with various boundary conditions, emphasizing the weak formulation and coercivity.

Elliptic Partial Differential Equations

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.

Embedding Theorems in Sobolev Spaces

Explores embedding theorems in Sobolev spaces, including continuous and compact embedding, weak convergence, and Poincaré inequality.

Weak Solutions of Differential Equations

Explores weak solutions of differential equations and their properties.

Weak Formulation of Elliptic PDEs

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

Embedding Theorems in Sobolev Spaces

Explores weak convergence, Poincaré inequality, and embedding theorems in Sobolev spaces.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Interior Regularity Results

Explores interior regularity results, focusing on weak solutions and unique selection in mathematical analysis.

Sobolev Spaces and Continuous Embeddings

Covers Sobolev spaces, continuous embeddings, weak convergence, and Poincare inequalities.

Rigorous Proof of Differential Equations

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

Regularity of Weak Solutions

Explores elliptic PDEs, weak solutions, regularity, and strong solutions, with a focus on classical solutions and proof techniques.

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