Concept

Weak solution

Related lectures (22)

Discusses the conditions for a unique global solution to a given problem.

Introduces the Random-Subcube Model (RSM) for constraint satisfaction problems, exploring its structure, phase transitions, and variable freezing.

Interior Regularity Results

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

Finite Element Method: Weak Solutions

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

Integration by Parts in Sobolev Spaces

Explores integration by parts in Sobolev spaces and the Poincaré inequality in

W^{1,p}_0

with applications in PDEs.

Continuity and Galerkin Method

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

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.

Urban Sustainability Assessment

Explores urban sustainability assessment, focusing on decision-making for sustainable cities through approaches, solution spaces, and indicator selection.

Exact Fields, Direct Methods, Sobolev Spaces

Covers Hilbert's theorem, direct methods, and Sobolev spaces, including classical and modern methods.

Theoretical Study of Elliptic Partial Differential Equations

Covers the theoretical study of Elliptic Partial Differential Equations, including classical and weak solutions.

Linear Applications and Span

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Properties of Weak Derivatives

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

Extension of Linear Transformations

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Branch and Bound: Formal Description

Covers the Branch and Bound algorithm, focusing on formal description and implementation steps to find optimal integer solutions.

Optimization and Simulation

Explores greedy heuristics in optimization, integrality constraints, and comparison of optimization methods.

Distribution to Spaces: Interpolation and Continuity

Covers weak derivatives, interpolation spaces, and continuity in function spaces.

Diffusion Equations in Spherical Coordinates

Explores solving diffusion equations in steady state conditions for concentric spheres with fixed concentration and flux, emphasizing the importance of linearity and homogeneity.

Advanced analysis II: second order linear ODEs

Explores second-order linear ODEs, solutions uniqueness, and linear independence.

Elliptic Partial Differential Equations

Covers the theoretical study of Elliptic Partial Differential Equations, including electrostatics and advection-diffusion-reaction equations.

Distribution Interpolation Spaces

Explores distribution interpolation spaces, convergence of sequences, derivatives, weak derivatives, and their applications in minimization problems.