Agmon–Douglis–Nirenberg estimates

E588690

a priori estimate mathematical concept result in partial differential equations

Agmon–Douglis–Nirenberg estimates are fundamental a priori estimates in the theory of linear elliptic partial differential equations and systems, providing precise control of solution regularity in terms of data norms.

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Statements (47)

Predicate	Object
instanceOf	a priori estimate ⓘ mathematical concept ⓘ result in partial differential equations ⓘ
appliesTo	boundary value problems ⓘ linear elliptic partial differential equations ⓘ linear elliptic systems ⓘ
characterizes	regularity of solutions up to the boundary ⓘ
concerns	mixed-order elliptic systems ⓘ systems with different orders for different components ⓘ
controls	higher-order derivatives of solutions ⓘ norms of solutions in terms of norms of data ⓘ
describes	regularity of solutions of elliptic boundary value problems ⓘ
ensures	boundary regularity of solutions ⓘ gain of derivatives for solutions compared to data ⓘ interior regularity of solutions ⓘ
field	elliptic partial differential equations ⓘ elliptic systems ⓘ functional analysis ⓘ
framework	Hilbert space methods ⓘ Sobolev space theory ⓘ
generalizes	Schauder estimates NERFINISHED ⓘ classical elliptic regularity estimates ⓘ
implies	continuous dependence of solutions on data ⓘ existence of solutions under suitable assumptions ⓘ uniqueness of solutions under suitable assumptions ⓘ
isRelatedTo	Calderón–Zygmund estimates NERFINISHED ⓘ Gårding inequality NERFINISHED ⓘ Lax–Milgram theorem NERFINISHED ⓘ Schauder theory NERFINISHED ⓘ
isUsedIn	Fredholm theory for elliptic operators ⓘ elliptic systems arising in continuum mechanics ⓘ elliptic systems in mathematical physics ⓘ regularity theory for PDEs ⓘ the theory of linear elliptic boundary value problems ⓘ
namedAfter	Avron Douglis NERFINISHED ⓘ Louis Nirenberg NERFINISHED ⓘ Shmuel Agmon NERFINISHED ⓘ
provides	a priori bounds for solutions in Sobolev norms ⓘ
relates	solution norms to data norms ⓘ
requires	appropriate boundary conditions ⓘ ellipticity of the principal symbol ⓘ
significance	fundamental tool in modern elliptic PDE theory ⓘ
timePeriod	mid 20th century ⓘ
typicalDomain	bounded domains with smooth boundary ⓘ
uses	Sobolev spaces NERFINISHED ⓘ complementing boundary conditions ⓘ ellipticity conditions ⓘ

Referenced by (1)

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Louis Nirenberg → knownFor → Agmon–Douglis–Nirenberg estimates ⓘ