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Strongly Elliptic Systems and Boundary Integral Equations
, 2000Introduction 1. Abstract linear equations 2. Sobolev spaces 3. Strongly elliptic systems 4. Homogeneous distributions 5. Surface potentials 6. Boundary integral equations 7. The Laplace equation 8. The Helmholtz equation 9.
W. McLean
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Spectrum of an elliptic equation [PDF]
Mathematical Notes of the Academy of Sciences of the USSR, 1970 It is shown that the spectrum for the first boundary-value problem for a second-order elliptic equation always lies in the half-plane λ0 ≤Re z, where is the leading eigenvalue to which there corresponds a nonnegative eigenfunction. Apart from λ0, there are no other points of the spectrum on the straight line Re z=λ0.
V. B. Lidskii, A. G. Aslanyan
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Nonlinear Elliptic Equations of the Second Order
, 2016* Introduction* Linear elliptic equations* Quasilinear elliptic equations: Quasilinear uniformly elliptic equations* Mean curvature equations* Minimal surface equations* Fully nonlinear elliptic equations: Fully nonlinear uniformly elliptic equations ...
Qing Han
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Fully Nonlinear Elliptic Equations
, 1995Introduction Preliminaries Viscosity solutions of elliptic equations Alexandroff estimate and maximum principle Harnack inequality Uniqueness of solutions Concave equations $W^{2,p}$ regularity Holder regularity The Dirichlet problem for concave ...
L. Caffarelli, X. Cabré
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IBM Journal of Research and Development, 1967
A brief review is given of the literature on numerical methods for elliptic problems as reltaote tdh e ideas introduced by Courant, Friedrichs and Lewy in the fundamental paper published in Math. Ann. 100, 32 (1928). The discussion shows how the finitedifference methods have subsequently been extended and applied to higher order elliptic problems and ...
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A brief review is given of the literature on numerical methods for elliptic problems as reltaote tdh e ideas introduced by Courant, Friedrichs and Lewy in the fundamental paper published in Math. Ann. 100, 32 (1928). The discussion shows how the finitedifference methods have subsequently been extended and applied to higher order elliptic problems and ...
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Elliptic equations and Steiner symmetrization
Communications on Pure and Applied Mathematics, 1996We present a new proof of comparison results via Steiner symmetrization for solutions of elliptic equations. This proof relies upon a "level sets" argument.
ALVINO, ANGELO +3 more
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Russian Mathematical Surveys, 1960
This paper, like the note on integral geometry in the last number of the "Uspekhi" , is an addendum to my paper [1]. The main idea of the paper is contained in § 2, where we pose the problem of describing linear elliptic equations and their boundary problems in topological terms.
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This paper, like the note on integral geometry in the last number of the "Uspekhi" , is an addendum to my paper [1]. The main idea of the paper is contained in § 2, where we pose the problem of describing linear elliptic equations and their boundary problems in topological terms.
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1977
Publisher Summary This chapter discusses the elliptic equations. Equilibrium problems in two-dimensional and higher, continua give rise to elliptic partial differential equations. A prototype is the famous equation of Laplace is uxx + uyy + uzz = 0. This equation holds for the steady temperature in an isotropic medium, characterizes gravitational or ...
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Publisher Summary This chapter discusses the elliptic equations. Equilibrium problems in two-dimensional and higher, continua give rise to elliptic partial differential equations. A prototype is the famous equation of Laplace is uxx + uyy + uzz = 0. This equation holds for the steady temperature in an isotropic medium, characterizes gravitational or ...
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Elliptic Differential Equations: Theory and Numerical Treatment
, 20171 Partial Differential Equations and Their Classification Into Types.- 2 The Potential Equation.- 3 The Poisson Equation.- 4 Difference Methods for the Poisson Equation.- 5 General Boundary Value Problems.- 6 Tools from Functional Analysis.- 7 ...
W. Hackbusch
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, 2017
In this paper, combining with a new generalized ansätz and the fractional Jacobi elliptic equation, an improved fractional Jacobi elliptic equation method is proposed for seeking exact solutions of space‐time fractional partial differential equations ...
Qinghua Feng, F. Meng
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In this paper, combining with a new generalized ansätz and the fractional Jacobi elliptic equation, an improved fractional Jacobi elliptic equation method is proposed for seeking exact solutions of space‐time fractional partial differential equations ...
Qinghua Feng, F. Meng
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