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Super and ultracontractive bounds for doubly nonlinear evolution equations.

Matteo Bonforte, Gabriele Grillo (2006)

Revista Matemática Iberoamericana

We use logarithmic Sobolev inequalities involving the p-energy functional recently derived in [15], [21] to prove Lp-Lq smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form u· = Δp(um) (with m(p - 1) ≥ 1) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bound are of the form ||u(t)||q ≤ C||u0||rγ / tβ for any r ≤ q ∈ [1,+∞) and t > 0 and...

Superlinear elliptic boundary value problems

Ravindran Kannan, Rafael Ortega (1987)

Czechoslovak Mathematical Journal

Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps

Ferruccio Colombini, Ennio De Giorgi, Sergio Spagnolo (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Sur les équations invariantes par un groupe

A. Cerezo (1974/1975)

Séminaire Équations aux dérivées partielles (Polytechnique)

Sur une classe de problèmes d'évolution non linéaires et dégénérés

Michel Langlais (1984)

Journées équations aux dérivées partielles

Sur un'inéquation parabolique dans un ouvert non cylindrique

Marco Biroli (1975)

Rendiconti del Seminario Matematico della Università di Padova

Système d'inégalités aux différences finies du type elliptique

Marian Malec (1977)

Annales Polonici Mathematici

Systèmes mathématiques aux structures entremelées. Problèmes aux limites pour certains systèmes différentiels aux différences, ordinaires ou aux dérivées totales au sens de M. M. Picone

Mehmet Namik Oğuztöreli, Démètre J. Mangeron, S. Easwaran (1972)

Archivum Mathematicum

The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations

Xi Ting Liang, Wu Zaide (1997)

Commentationes Mathematicae Universitatis Carolinae

The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions.

The Calderón-Zygmund theory for elliptic problems with measure data

Giuseppe Mingione (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider non-linear elliptic equations having a measure in the right-hand side, of the type $div a (x, D u) = μ,$ and prove differentiability and integrability results for solutions. New estimates in Marcinkiewicz spaces are also given, and the impact of the measure datum density properties on the regularity of solutions is analyzed in order to build a suitable Calderón-Zygmund theory for the problem. All the regularity results presented in this paper are provided together with explicit local a priori estimates.

The coercitivity of elliptic sesquilinear forms on the Sobolev spaces $[W_{2}^{(} s) (Ω)]^{M}$ [Abstract of thesis]

Van Khuong Vu (1988)

Commentationes Mathematicae Universitatis Carolinae

The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Björn E. J. Dahlberg, C. E. Kenig, G. C. Verchota (1986)

Annales de l'institut Fourier

In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator $Δ^{2}$ , on an arbitrary bounded Lipschitz domain $D$ in $R^{n}$ . We establish existence and uniqueness results when the boundary values have first derivatives in $L^{2} (\partial D)$ , and the normal derivative is in $L^{2} (\partial D)$ . The resulting solution $u$ takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of $\nabla u$ is shown to be in $L^{2} (\partial D)$ .

The Dirichlet problem in weighted spaces on a dihedral domain

Adam Kubica (2009)

Banach Center Publications

We examine the Dirichlet problem for the Poisson equation and the heat equation in weighted spaces of Kondrat'ev's type on a dihedral domain. The weight is a power of the distance from a distinguished axis and it depends on the order of the derivative. We also prove a priori estimates.

The elliptic problems in a family of planar open sets

Abdelkader Tami (2019)

Applications of Mathematics

We propose, on a model case, a new approach to classical results obtained by V. A. Kondrat'ev (1967), P. Grisvard (1972), (1985), H. Blum and R. Rannacher (1980), V. G. Maz'ya (1980), (1984), (1992), S. Nicaise (1994a), (1994b), (1994c), M. Dauge (1988), (1990), (1993a), (1993b), A. Tami (2016), and others, describing the singularities of solutions of an elliptic problem on a polygonal domain of the plane that may appear near a corner. It provides a more precise description of how the solutions...

The energy method for a class of hyperbolic equations

Enrico Jannelli (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota viene introdotto un nuovo metodo per ottenere espressioni esplicite dell'energia della soluzione dell'equazione iperbolica $\left(\frac{\partial}{\partial t}\right)^{m}u+\sum_{|\nu|+j\leq m\,;\,j\leq m-% 1}a_{\nu,j}(t)\,\left(\frac{\partial}{\partial x}\right)^{\nu}\left(\frac{% \partial}{\partial t}\right)^{j}u=0.$ Stimando opportunamente queste espressioni si ottengono nuovi risultati di buona positura negli spazi di Gevrey per l'equazione $(\cdot)$ quando questa è debolmente iperbolica.

The equation $\nabla_{2}u+a_{10}(x,y)\frac{\partial u}{\partial x}+a_{01}(x,y)\frac{\partial u% }{\partial y}+a_{00}(x,y)u=F(x,y)$ . Estimates connected to boundary value problems

Alberto Cialdea (1986)