Noether boundary value problems
E770192
Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
class of boundary value problems
ⓘ
concept in partial differential equations ⓘ mathematical concept ⓘ |
| aimsAt |
establishing conditions for unique solvability up to finite-dimensional spaces
ⓘ
formulating boundary conditions that yield Fredholm operators ⓘ |
| appliesTo |
elliptic partial differential equations
ⓘ
linear partial differential equations ⓘ |
| characterizedBy |
Fredholm-type properties
ⓘ
boundary conditions ensuring well-posedness ⓘ finite-dimensional solution spaces ⓘ index theory considerations ⓘ |
| concerns |
classification of admissible boundary conditions
ⓘ
compatibility conditions for boundary data ⓘ |
| context |
classical theory of boundary value problems
ⓘ
theory of linear operators in Banach and Hilbert spaces ⓘ |
| developedBy | Fritz Noether NERFINISHED ⓘ |
| ensures |
existence of solutions under suitable conditions
ⓘ
finite-dimensional kernel and cokernel of associated operators ⓘ |
| field |
functional analysis
ⓘ
mathematical physics ⓘ partial differential equations ⓘ |
| formalism | operator-theoretic description of boundary conditions ⓘ |
| hasAspect |
analysis of cokernels of differential operators
ⓘ
analysis of kernels of differential operators ⓘ study of adjoint boundary value problems ⓘ study of compatibility conditions for inhomogeneous terms ⓘ |
| hasProperty |
admit a finite-dimensional space of obstructions
ⓘ
admit a finite-dimensional space of solutions ⓘ solutions are unique up to a finite-dimensional kernel ⓘ solutions depend continuously on boundary data ⓘ |
| historicalPeriod | early 20th century ⓘ |
| influenced |
development of index theory for differential operators
ⓘ
modern theory of elliptic boundary value problems ⓘ |
| involves |
analysis of linear operators between function spaces
ⓘ
study of solvability conditions ⓘ |
| namedAfter | Fritz Noether NERFINISHED ⓘ |
| relatedTo |
Fredholm operators
NERFINISHED
ⓘ
Lopatinskii–Shapiro condition NERFINISHED ⓘ elliptic boundary conditions ⓘ elliptic boundary value problems ⓘ index of an operator ⓘ well-posedness of boundary value problems ⓘ |
| usedIn |
mathematical formulation of physical boundary conditions
ⓘ
spectral theory of differential operators ⓘ theory of elliptic operators on bounded domains ⓘ |
Referenced by (1)
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