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Hilbert's nineteenth problem, the Glossary

Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled by David Hilbert in 1900.^[1]

43 relations: A priori estimate, American Journal of Mathematics, American Mathematical Society, Analytic function, Émile Picard, Basel, Bologna, Bulletin of the American Mathematical Society, Calculus of variations, Counterexample, David Hilbert, Derivative, Differentiable function, Elliptic partial differential equation, Ennio De Giorgi, Euler–Lagrange equation, Functional (mathematics), Gaussian curvature, Gradient, Hölder condition, Hessian matrix, Hilbert's problems, International Congress of Mathematicians, Italian Mathematical Union, Italic type, John Forbes Nash Jr., Joseph Liouville, L'Enseignement mathématique, Laplace's equation, Liouville's equation, Lipschitz continuity, Mary Frances Winston Newson, Matematicheskii Sbornik, Mathematische Annalen, Maximum and minimum, Minimal surface, Partial differential equation, Potential theory, Proceedings of the National Academy of Sciences of the United States of America, Regularity theory, River Edge, New Jersey, Springer Science+Business Media, Weak derivative.
Hilbert's problems

A priori estimate

In the theory of partial differential equations, an a priori estimate (also called an apriori estimate or a priori bound) is an estimate for the size of a solution or its derivatives of a partial differential equation. Hilbert's nineteenth problem and a priori estimate are partial differential equations.

See Hilbert's nineteenth problem and A priori estimate

American Journal of Mathematics

The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

See Hilbert's nineteenth problem and American Mathematical Society

Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

See Hilbert's nineteenth problem and Analytic function

Émile Picard

Charles Émile Picard (24 July 1856 – 11 December 1941) was a French mathematician.

See Hilbert's nineteenth problem and Émile Picard

Basel

Basel, also known as Basle,Bâle; Basilea; Basileia; other Basilea.

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Bologna

Bologna (Bulåggna; Bononia) is the capital and largest city of the Emilia-Romagna region, in northern Italy.

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Bulletin of the American Mathematical Society

The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.

See Hilbert's nineteenth problem and Bulletin of the American Mathematical Society

Calculus of variations

The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

See Hilbert's nineteenth problem and Calculus of variations

Counterexample

A counterexample is any exception to a generalization.

See Hilbert's nineteenth problem and Counterexample

David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of his time.

See Hilbert's nineteenth problem and David Hilbert

Derivative

The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input.

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Differentiable function

In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

See Hilbert's nineteenth problem and Differentiable function

Elliptic partial differential equation

Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Hilbert's nineteenth problem and elliptic partial differential equation are partial differential equations.

See Hilbert's nineteenth problem and Elliptic partial differential equation

Ennio De Giorgi

Ennio De Giorgi (8 February 1928 – 25 October 1996) was an Italian mathematician who worked on partial differential equations and the foundations of mathematics.

See Hilbert's nineteenth problem and Ennio De Giorgi

Euler–Lagrange equation

In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. Hilbert's nineteenth problem and Euler–Lagrange equation are calculus of variations and partial differential equations.

See Hilbert's nineteenth problem and Euler–Lagrange equation

Functional (mathematics)

In mathematics, a functional is a certain type of function.

See Hilbert's nineteenth problem and Functional (mathematics)

Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, and, at the given point: K.

See Hilbert's nineteenth problem and Gaussian curvature

Gradient

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase.

See Hilbert's nineteenth problem and Gradient

Hölder condition

In mathematics, a real or complex-valued function on -dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there are real constants,, such that | f(x) - f(y) | \leq C\| x - y\|^ for all and in the domain of.

See Hilbert's nineteenth problem and Hölder condition

Hessian matrix

In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.

See Hilbert's nineteenth problem and Hessian matrix

Hilbert's problems

Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900.

See Hilbert's nineteenth problem and Hilbert's problems

International Congress of Mathematicians

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics.

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Italian Mathematical Union

The Italian Mathematical Union (Unione Matematica Italiana) is a mathematical society based in Italy.

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Italic type

In typography, italic type is a cursive font based on a stylised form of calligraphic handwriting.

See Hilbert's nineteenth problem and Italic type

John Forbes Nash Jr.

John Forbes Nash, Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations.

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Joseph Liouville

Joseph Liouville (24 March 1809 – 8 September 1882) was a French mathematician and engineer.

See Hilbert's nineteenth problem and Joseph Liouville

L'Enseignement mathématique

L’Enseignement mathématique is a journal for mathematics and mathematics education.

See Hilbert's nineteenth problem and L'Enseignement mathématique

Laplace's equation

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.

See Hilbert's nineteenth problem and Laplace's equation

Liouville's equation

In differential geometry, Liouville's equation, named after Joseph Liouville, is the nonlinear partial differential equation satisfied by the conformal factor of a metric on a surface of constant Gaussian curvature: where is the flat Laplace operator.

See Hilbert's nineteenth problem and Liouville's equation

Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions.

See Hilbert's nineteenth problem and Lipschitz continuity

Mary Frances Winston Newson

Mary Frances Winston Newson (August 7, 1869 December 5, 1959) was an American mathematician.

See Hilbert's nineteenth problem and Mary Frances Winston Newson

Matematicheskii Sbornik

Matematicheskii Sbornik (Математический сборник, abbreviated Mat. Sb.) is a peer reviewed Russian mathematical journal founded by the Moscow Mathematical Society in 1866.

See Hilbert's nineteenth problem and Matematicheskii Sbornik

Mathematische Annalen

Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.

See Hilbert's nineteenth problem and Mathematische Annalen

Maximum and minimum

In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function.

See Hilbert's nineteenth problem and Maximum and minimum

Minimal surface

In mathematics, a minimal surface is a surface that locally minimizes its area.

See Hilbert's nineteenth problem and Minimal surface

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. Hilbert's nineteenth problem and partial differential equation are partial differential equations.

See Hilbert's nineteenth problem and Partial differential equation

Potential theory

In mathematics and mathematical physics, potential theory is the study of harmonic functions. Hilbert's nineteenth problem and potential theory are partial differential equations.

See Hilbert's nineteenth problem and Potential theory

Proceedings of the National Academy of Sciences of the United States of America

Proceedings of the National Academy of Sciences of the United States of America (often abbreviated PNAS or PNAS USA) is a peer-reviewed multidisciplinary scientific journal.

See Hilbert's nineteenth problem and Proceedings of the National Academy of Sciences of the United States of America

Regularity theory

Regularity is a property of elliptic partial differential equations such as Laplace's equation.

See Hilbert's nineteenth problem and Regularity theory

River Edge, New Jersey

River Edge is a borough in Bergen County, in the U.S. state of New Jersey.

See Hilbert's nineteenth problem and River Edge, New Jersey

Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

See Hilbert's nineteenth problem and Springer Science+Business Media

Weak derivative

In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the L''p'' space L^1().

See Hilbert's nineteenth problem and Weak derivative

References

[1] https://en.wikipedia.org/wiki/Hilbert's_nineteenth_problem

Also known as Hilbert's 19th problem.

Hilbert's nineteenth problem, the Glossary

Table of Contents

See also

Hilbert's problems

References