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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.".
- Schauder_estimates wikiPageExternalLink sm516.pdf.
- Schauder_estimates wikiPageExternalLink l5151uv221520628.
- Schauder_estimates wikiPageID "23547303".
- Schauder_estimates wikiPageRevisionID "569968855".
- 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 year "1934".
- Schauder_estimates year "1937".
- Schauder_estimates year "1983".
- Schauder_estimates subject Category:Elliptic_partial_differential_equations.
- Schauder_estimates type Abstraction100002137.
- Schauder_estimates type Communication100033020.
- Schauder_estimates type DifferentialEquation106670521.
- Schauder_estimates type EllipticPartialDifferentialEquations.
- Schauder_estimates type Equation106669864.
- Schauder_estimates type MathematicalStatement106732169.
- Schauder_estimates type Message106598915.
- Schauder_estimates type PartialDifferentialEquation106670866.
- Schauder_estimates type Statement106722453.
- 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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