Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators

Dario Daniele Monticelli

Displaying similar documents to “Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators”

Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations

Guy Barles, Emmanuel Chasseigne, Cyril Imbert (2011)

Journal of the European Mathematical Society

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This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity...

A Liouville-type theorem for elliptic systems

D. G. De Figueiredo, P. L. Felmer (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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A nonlocal elliptic equation in a bounded domain

Piotr Fijałkowski, Bogdan Przeradzki, Robert Stańczy (2004)

Banach Center Publications

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The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $- \sum_{i, j = 1}^{n} D_{i} (a_{i j} D_{j} u) = f (u, \int_{Ω} g (u^{p}))$ , in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel’skiĭ Fixed Point Theorem enables us to find many solutions as well.

On positive solutions of quasilinear elliptic systems

Yuanji Cheng (1997)

Czechoslovak Mathematical Journal

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In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems $\}\begin{matrix} - Δ_{p} u = f (x, u, v), & in Ω, - Δ_{p} v = g (x, u, v), & in Ω, u = v = 0, & on \partial Ω, \end{matrix}$ where $- Δ_{p}$ is the $p$ -Laplace operator, $p > 1$ and $Ω$ is a $C^{1, α}$ -domain in $ℝ^{n}$ . We prove an analogue of [7, 16] for the eigenvalue problem with $f (x, u, v) = λ_{1} v^{p - 1}$ , $g (x, u, v) = λ_{2} u^{p - 1}$ and obtain a non-existence result of positive solutions for the general systems.

$L^{p, Φ}$ spaces and their application to elliptic partial differential operators

Magdalena Jaroszewska (1983)

Annales Polonici Mathematici

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On the principal eigenvalue of elliptic operators in $ℝ^{N}$ and applications

Henry Berestycki, Luca Rossi (2006)

Journal of the European Mathematical Society

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Two generalizations of the notion of principal eigenvalue for elliptic operators in $ℝ^{N}$ are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.

Partially elliptic pseudodifferential operators and the $W F_{x}$ of distributions

Annalisa Menegus, Giuseppe Olivi (1976)

Rendiconti del Seminario Matematico della Università di Padova

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A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media

Guillermo Reyes, Juan Luis Vázquez (2006)

Journal of the European Mathematical Society

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In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution $u$ of an elliptic equation, that we write $u^{*}$ , can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the...

Levi's parametrix for some sub-elliptic non-divergence form operators.

Bonfiglioli, Andrea, Lanconelli, Ermanno, Uguzzoni, Francesco (2003)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Uniqueness of solutions for some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2014)

Applicationes Mathematicae

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We investigate the existence and uniqueness of solutions to the Dirichlet problem for a degenerate nonlinear elliptic equation $- \sum_{i, j = 1}^{n} D_{j} (a_{i j} (x) D_{i} u (x)) + b (x) u (x) + d i v (Φ (u (x))) = g (x) - \sum_{j = 1}^{n} f_{j} (x)$ on Ω in the setting of the space H₀(Ω).

Elliptic and degenerate-elliptic operators in unbounded domains

D. E. Edmunds, W. D. Evans (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On a semilinear elliptic equation in $ℍ^{n}$

Gianni Mancini, Kunnath Sandeep (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.

On a semilinear elliptic eigenvalue problem

Mario Michele Coclite (1997)

Annales Polonici Mathematici

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We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, ${u |}_{\partial Ω} = 0$ , where f(x) and h(u) satisfy minimal regularity assumptions.

A characterization of elliptic operators

Grzegorz Łysik, Paweł M. Wójcicki (2014)

Annales Polonici Mathematici

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We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.