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- Schauder_estimates abstract "In mathematics, the Schauder estimates are a collection of results due to Juliusz Schauder (1934, 1937) concerning the regularity of solutions to linear, uniformly elliptic partial differential equations. The estimates say that when the equation has appropriately smooth terms and appropriately smooth solutions, then the Hölder norm of the solution can be controlled in terms of the Hölder norms for the coefficient and source terms. Since these estimates do not assume the existence of the solution, they are called a priori estimates.There is both an interior result, giving a Hölder condition for the solution in interior domains away from the boundary, and a boundary result, giving the Hölder condition for the solution in the entire domain. The former bound depends only on the spatial dimension, the equation, and the distance to the boundary; the latter depends on the smoothness of the boundary as well.The Schauder estimates are a necessary precondition to using the method of continuity to proving the existence and regularity of solutions to the Dirichlet problem for elliptic PDEs. This result says that when the coefficients of the equation and the nature of the boundary conditions are sufficiently smooth, there is a smooth classical solution to the PDE.".
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- Schauder_estimates wikiPageWikiLink A_priori_estimate.
- Schauder_estimates wikiPageWikiLink Category:Elliptic_partial_differential_equations.
- Schauder_estimates wikiPageWikiLink Courant_Institute_of_Mathematical_Sciences.
- Schauder_estimates wikiPageWikiLink Differentiable.
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- Schauder_estimates wikiPageWikiLink Dirichlet_problem.
- Schauder_estimates wikiPageWikiLink Elliptic_operator.
- Schauder_estimates wikiPageWikiLink Hölder_condition.
- Schauder_estimates wikiPageWikiLink Mathematics.
- Schauder_estimates wikiPageWikiLink Maximum_principle.
- Schauder_estimates wikiPageWikiLink Method_of_continuity.
- Schauder_estimates wikiPageWikiLink Multi-index_notation.
- Schauder_estimates wikiPageWikiLink Partial_differential_equation.
- Schauder_estimates wikiPageWikiLinkText "Schauder estimates".
- Schauder_estimates wikiPageWikiLinkText "a priori estimates".
- Schauder_estimates authorLink "Juliusz Schauder".
- Schauder_estimates authorlink "Neil Trudinger".
- Schauder_estimates first "D.".
- Schauder_estimates first "Juliusz".
- Schauder_estimates first "Neil".
- Schauder_estimates hasPhotoCollection Schauder_estimates.
- Schauder_estimates last "Gilbarg".
- Schauder_estimates last "Schauder".
- Schauder_estimates last "Trudinger".
- Schauder_estimates wikiPageUsesTemplate Template:Citation.
- Schauder_estimates wikiPageUsesTemplate Template:Harvs.
- Schauder_estimates wikiPageUsesTemplate Template:MathSciNet.
- Schauder_estimates year "1934".
- Schauder_estimates year "1937".
- Schauder_estimates year "1983".
- Schauder_estimates subject Category:Elliptic_partial_differential_equations.
- Schauder_estimates hypernym Collection.
- Schauder_estimates type Book.
- Schauder_estimates comment "In mathematics, the Schauder estimates are a collection of results due to Juliusz Schauder (1934, 1937) concerning the regularity of solutions to linear, uniformly elliptic partial differential equations. The estimates say that when the equation has appropriately smooth terms and appropriately smooth solutions, then the Hölder norm of the solution can be controlled in terms of the Hölder norms for the coefficient and source terms.".
- Schauder_estimates label "Schauder estimates".
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- Schauder_estimates sameAs Q7430990.
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