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We give a structure result for the positive radial solutions of the following equation: $Δ_{p} u + K (r) u {| u |}^{q - 1} = 0$ with some monotonicity assumptions on the positive function $K (r)$ . Here $r = | x |$ , $x \in ℝ^{n}$ ; we consider the case when $n > p > 1$ , and $q > p_{*} = \frac{n (p - 1)}{n - p}$ . We continue the discussion started by Kawano et al. in [KYY], refining the estimates on the asymptotic behavior of Ground States with slow decay and we state the existence of S.G.S., giving also for them estimates on the asymptotic behavior, both as $r \to 0$ and as $r \to \infty$ . We make use of a Emden-Fowler transform...

Completely semielliptic boundary value problems

Artino, Ralph A. (1993)

Portugaliae mathematica

Complex vector fields and hypoelliptic partial differential operators

Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten (2010)

Annales de l’institut Fourier

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields.Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators.Finally we describe a class of compact homogeneous CR manifolds for which the distribution of $(0, 1)$ vector fields satisfies...

Correction to the paper: $C^{1, α}$ local regularity for the solutions of the p-Laplacian on the Heisenberg group. The case $1 + \frac{1}{\sqrt{5}} < p \leq 2$

Silvana Marchi (2003)

Commentationes Mathematicae Universitatis Carolinae

Criteria for hypoellipticity

Y. Morimoto (1986/1987)

Séminaire Équations aux dérivées partielles (Polytechnique)

Degree theory for VMO maps on metric spaces

Francesco Uguzzoni, Ermanno Lanconelli (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We construct a degree theory for Vanishing Mean Oscillation functions in metric spaces, following some ideas of Brezis & Nirenberg. The underlying sets of our metric spaces are bounded open subsets of $ℝ^{N}$ and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the $L$ -harmonic extensions of VMO vector-valued functions. The operators $L$ we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity...

Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale

Gérard Ben Arous (1989)

Annales de l'institut Fourier

On obtient ici le développement asymptotique, en temps petit et sur la diagonale, du noyau de la chaleur associé à un opérateur dégénéré du second ordre satisfaisant à la condition forte d’hypoellipticité de Hörmander.

Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus

G. Ben Arous (1988)

Annales scientifiques de l'École Normale Supérieure

Differentiability and growth of solutions of partial differential equations.

Michael Langenbruch (1982)

Manuscripta mathematica

Dirichlet problem with L $^{p}$ -boundary data in contractible domains of Carnot groups

Andrea Bonfiglioli, Ermanno Lanconelli (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $ℒ$ be a sub-laplacian on a stratified Lie group $G$ . In this paper we study the Dirichlet problem for $ℒ$ with $L^{p}$ -boundary data, on domains $Ω$ which are contractible with respect to the natural dilations of $G$ . One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for $ℒ$ . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.

Dispersive and Strichartz estimates on H-type groups

Martin Del Hierro (2005)

Studia Mathematica

Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in [1], to H-type groups. On those groups we get optimal time decay for solutions to the wave equation (decay as $t^{- p / 2}$ ) and the Schrödinger equation (decay as $t^{(1 - p) / 2}$ ), p being the dimension of the center of the group. As a corollary, we obtain the corresponding Strichartz inequalities for the wave equation, and, assuming that p > 1, for the Schrödinger equation.

Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics

Michael Hitrik, Karel Pravda-Starov (2013)

Annales de l’institut Fourier

For a class of non-selfadjoint $h$ –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...

Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales

Gilles Lebeau (2007)

Annales de l’institut Fourier

Nous donnons des résultats analytiques sur les propriétés de régularité du laplacien hypoelliptique de Jean-Michel Bismut et plus généralement sur les opérateurs $P$ de type Fokker-Planck géométrique agissant sur le fibré cotangent $Σ = T^{*} X$ d’une variété riemannienne compacte $X$ . En particulier, nous prouvons un résultat d’hypoellipticité maximale pour $P$ , et nous en déduisons des bornes sur la localisation de ses valeurs spectrales.

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Boundary value problems for quasielliptic systems.

Calcul pseudodifférentiel trois-étape

Caratterizzazione dei sistemi ipoellittici a coefficienti costanti, sovradeterminati, con il metodo della paramatrice

Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations.

Classification of positive solutions of $p$ -Laplace equation with a growth term

Completely semielliptic boundary value problems

Complex vector fields and hypoelliptic partial differential operators

Correction to the paper: $C^{1, α}$ local regularity for the solutions of the p-Laplacian on the Heisenberg group. The case $1 + \frac{1}{\sqrt{5}} < p \leq 2$

Criteria for hypoellipticity

Degree theory for VMO maps on metric spaces

Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale

Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus

Differentiability and growth of solutions of partial differential equations.

Dirichlet problem with L $^{p}$ -boundary data in contractible domains of Carnot groups

Dispersive and Strichartz estimates on H-type groups

Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics

Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales

Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs.

Estimates of the higher order derivatives of the solutions of hypoelliptic equations.

Estimations de Strichartz généralisées sur le groupe de Heisenberg

Currently displaying 21 – 40 of 181