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The spectrum of an elliptic equation
Mathematical Notes of the Academy of Sciences of the USSR, 1972In this paper we consider conditions for the presence or absence of spectral points in the left complex halfplane of a general second-order elliptic operator.
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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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Acta Mathematica Scientia, 2002
The following eigen-value problem of the Hermite nonlinear elliptic equation \[ -\Delta u+x^2u=\lambda f(x,u),\quad u\in H^1(\mathbb R^n),\tag{*} \] where \(f(x,u)\) is nondecreasing, Lipschitz and \(|f(x,t)|\leq c|t|^q ...
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The following eigen-value problem of the Hermite nonlinear elliptic equation \[ -\Delta u+x^2u=\lambda f(x,u),\quad u\in H^1(\mathbb R^n),\tag{*} \] where \(f(x,u)\) is nondecreasing, Lipschitz and \(|f(x,t)|\leq c|t|^q ...
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On elliptic equations with an axial symmetry [PDF]
Annali di Matematica Pura ed Applicata, 1981 Si considera l'equazione (*) auxx+2buxy+cuyy+(d/y)uy=f dove a, b, c, d e L∞, d > 0, f e L2. Supponendo che (*) sia uniformemente eliittica e che l'oscillazione del quoziente d/a verifichi una resirizione vicino all'asse della x, si provano stime a priori e un teorema di esistenza per soluzioni W2,2 di un problema di Dirichlet relativo all'equazione (*).
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1996
Methods of the calculus of variations applied to problems in geometry and classical continuum mechanics often lead to elliptic PDE that are not linear. We discuss a number of examples and some of the developments that have arisen to treat such problems.
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Methods of the calculus of variations applied to problems in geometry and classical continuum mechanics often lead to elliptic PDE that are not linear. We discuss a number of examples and some of the developments that have arisen to treat such problems.
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1996
The first major topic of this chapter is the Dirichlet problem for the Laplace operator on a compact domain with boundary: $$\Delta u = 0\text{ on }\Omega,\quad {u\bigr |}_{\partial\Omega } = f.$$ (0.1) We also consider the nonhomogeneous problem Δu = g and allow for lower-order terms. As in Chap.
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The first major topic of this chapter is the Dirichlet problem for the Laplace operator on a compact domain with boundary: $$\Delta u = 0\text{ on }\Omega,\quad {u\bigr |}_{\partial\Omega } = f.$$ (0.1) We also consider the nonhomogeneous problem Δu = g and allow for lower-order terms. As in Chap.
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Oscillation Theorems for Elliptic Equations [PDF]
Proceedings of the American Mathematical Society, 1964 We shall assume that the coefficients of all equations of the form (1) satisfy (i) aij(x) differentiable, c(x) continuous; (ii) aij=d2ji, c =c; (iii) Eaijtijj > 0 for all complex n-tuples ((, , n) # (0, , 0) in a smooth bounded domain G CE'. If the coefficients of (1) can be extended into a larger domain G'DG so that (i)-(iii) hold in G as well as G ...
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2009
We give an introduction to elliptic curves over the rationals and present classical and modern methods for finding integer points on elliptic curves.
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We give an introduction to elliptic curves over the rationals and present classical and modern methods for finding integer points on elliptic curves.
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ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS
Mathematics of the USSR-Sbornik, 1971A linear differential operator in of elliptic type, with varying coefficients, is considered along with a boundary value problem for such an operator in the exterior of a bounded region. Certain conditions on the symbol of the operator are assumed, the formulation of which involves lower-order terms.
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New Creatinine- and Cystatin C–Based Equations to Estimate GFR without Race
New England Journal of Medicine, 2021Lesley A Inker +2 more
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