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In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling , elliptic PDEs are frequently used to model steady states , unlike parabolic PDE and hyperbolic PDE which generally model phenomena that change in time.
Gilbarg was co-author, together with his student Neil Trudinger, of the book Elliptic Partial Differential Equations of Second Order. Besides Trudinger, Gilbarg's doctoral students include Jerald Ericksen and James Serrin.
In mathematics, and more precisely, in functional Analysis and PDEs, 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.
Heinz Otto Cordes (March 18, 1925 – October 30, 2018) was a German-American mathematician, specializing in partial differential equations (PDEs). [1] He is known for the Aronszajn–Cordes uniqueness theorem for solutions of elliptic PDEs (due independently to Nachman Aronszajn). [2] [3] [4]
Pages in category "Elliptic partial differential equations" The following 19 pages are in this category, out of 19 total. This list may not reflect recent changes .
In 1971, James Serrin utilized Alexandrov's technique to prove that highly symmetric solutions of certain second-order elliptic partial differential equations must be supported on symmetric domains. Nirenberg realized that Serrin's work could be reformulated so as to prove that solutions of second-order elliptic partial differential equations ...
In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which implies the key property that the principal symbol is invertible, or equivalently that there are no real ...
These papers were among the first to develop a general theory of second-order elliptic differential equations which are fully nonlinear, with a regularity theory that extends to the boundary. Caffarelli, Nirenberg & Spruck (1985) has been particularly influential in the field of geometric analysis since many geometric partial differential ...
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