Linked from

The 26 pages that link to Sobolev space, each with the reason it gives.

• Hilbert spaceBroader topic: Sobolev spaces are Hilbert spaces central to weak solutions of differential equations.

• GradientRelated: Sobolev spaces provide a setting where gradients exist in a generalized sense.

• Banach spaceBroader topic: Its standard norms make Sobolev spaces Banach spaces used in differential equations.

• LaplacianRelated: Sobolev spaces provide a setting for weak solutions when classical derivatives fail.

• Functional analysisBroader topic: Sobolev spaces make weak solutions of differential equations mathematically precise.

• Lp spaceRelated: Its defining integrability conditions are built from Lp spaces.

• Distribution (mathematics)Related: Sobolev spaces use distributional derivatives while imposing additional integrability.

• Weak solutionNarrower topic: Many weak solutions are sought in Sobolev spaces that control both values and weak derivatives.

• Dirichlet boundary conditionRelated: Sobolev traces let Dirichlet data be defined for solutions lacking classical boundary smoothness.

• Dirichlet problemRelated: Sobolev spaces give a framework for weak solutions and boundary traces.

• Stefan BanachRelated: Sobolev spaces apply Banach-space methods to differential equations.

• Distribution theoryRelated: Weak derivatives connect distribution theory to the function spaces used in partial differential equations.

• Elliptic regularityRelated: Elliptic estimates commonly show that weak solutions belong to higher-order Sobolev spaces.

• Weak derivativeBroader topic: Sobolev spaces collect functions according to the integrability of their weak derivatives.

• Absolute continuityRelated: In one dimension, Sobolev functions have absolutely continuous representatives on bounded intervals.

• Direct method in the calculus of variationsRelated: Sobolev spaces provide common admissible spaces with useful compactness and semicontinuity properties.

• Elliptic operatorRelated: Elliptic estimates compare solution regularity across Sobolev spaces.

• Geometric analysisRelated: Weak solutions to geometric equations are often sought in Sobolev spaces.

• Sobolev inequalityNarrower topic: The inequality compares norms that define these spaces.

• Wirtinger's inequalityNarrower topic: The inequality extends naturally from smooth periodic functions to Sobolev functions.

• Karen UhlenbeckRelated: Sobolev spaces let geometric analysts control fields whose derivatives may not be classically smooth.

• Rademacher's theoremRelated: Lipschitz functions have bounded weak derivatives, linking classical and weak differentiation.

• Agmon's inequalityNarrower topic: The inequality's input and output are norms on Sobolev spaces.

• Cathleen Synge MorawetzRelated: Sobolev norms provide the regularity framework for many nonlinear PDE results.

• Friedrichs' inequalityNarrower topic: Friedrichs' inequality is typically stated for functions in these spaces.

• Peetre's inequalityRelated: Frequency weights in Sobolev estimates can be compared across sums using Peetre's bound.