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$L_{2}$ -оценки решений общих краевых задач для уравнения со смешанной парабoло-эллиптической структурой

М.А. Абдрахманов (1992)

Zapiski naucnych seminarov POMI

$L_{\infty}$ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_{\infty}$ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_{\infty}$ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_{\infty}$ -estimates are obtained by the Di Benedetto methods.

$L^{\infty}$ -estimates for nonlinear elliptic problems with $p$ -growth in the gradient.

Ferone, V., Posteraro, M.R., Rakotoson, J.M. (1999)

Journal of Inequalities and Applications [electronic only]

$L^{\infty}$ -estimates for nonlinear parabolic equations with natural growth conditions

Vincenzo Vespri (1993)

Rendiconti del Seminario Matematico della Università di Padova

$L^{\infty}$ estimates of solution for $m$ -Laplacian parabolic equation with a nonlocal term

Pulun Hou, Caisheng Chen (2011)

Czechoslovak Mathematical Journal

In this paper, we consider the global existence, uniqueness and $L^{\infty}$ estimates of weak solutions to quasilinear parabolic equation of $m$ -Laplacian type $u_{t} - {div (| \nabla u |}^{m - 2} {\nabla u) = u | u |}^{β - 1} \int_{Ω} {| u |}^{α} d x$ in $Ω \times (0, \infty)$ with zero Dirichlet boundary condition in $\partial Ω$ . Further, we obtain the $L^{\infty}$ estimate of the solution $u (t)$ and $\nabla u (t)$ for $t > 0$ with the initial data $u_{0} \in L^{q} (Ω)$ $(q > ...$

$L^{p}$ -estimates for hyperbolic operators applications to $□ u = u^{k}$

I. Peral, J. C. Peral, M. Walias (1982)

Annales de la Faculté des sciences de Toulouse : Mathématiques

$L^{p}$ -Estimates for linear elliptic systems with discontinuous coefficients

Filippo Chiarenza, Michelangelo Franciosi, Michele Frasca (1994)

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

In this Note we give $L^{p}$ estimates $(1 < p < + \infty)$ for the highest order derivatives of an elliptic system in non-divergence form with coefficients in VMO.

$L_{p}$ -estimates for solutions of Dirichlet and Neumann problems to heat equation in the wedge with edge of arbitrary codimension

Nazarov, Alexander I. (2002)

Equadiff 10

$L^{p}$ estimates for the wave equation and applications

Christopher D. Sogge (1993)

Journées équations aux dérivées partielles

$L^{p} - L^{q}$ time decay estimates for the solution of the linear partial differential equations of thermodiffusion

Arkadiusz Szymaniec (2010)

Applicationes Mathematicae

We consider the initial-value problem for a linear hyperbolic parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove $L^{p} - L^{q}$ time decay estimates for the solution of the associated linear Cauchy problem.

$L^{p}$ -oценки решений задачи Коши для одномерного гиперболического уравнения

А.В. Пержан (1983)

Matematiceskie issledovanija

$L_{p}$ -oценки решения задачи Коши для одномерного гиперболического уравнения высокого порядка с постоянными коэффициентами

Ю.И. Балтаг (1987)

Matematiceskie issledovanija

$L_{p}$ - theory for a class of singular elliptic differential operators, II

Hans Kretschmer, Hans Triebel (1976)

Czechoslovak Mathematical Journal

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

Magdalena Jaroszewska (1983)

Annales Polonici Mathematici

$L_{p}$ -оценки решения смешанной задачи с условиями Дирихле для волнового уравнения при радиальных начальных данных

А.Ф. Мустяца (1987)

Matematiceskie issledovanija

$L^{q}$ estimates for damped wave equations with odd initial data.

Narazaki, Takashi (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

L1 and L∞-estimates with a local weight for the ∂-equation on convex domains in Cn.

Francesc Tugores (1992)

Publicacions Matemàtiques

We construct a defining function for a convex domain in Cn that we use to prove that the solution-operator of Henkin-Romanov for the ∂-equation is bounded in L1 and L∞-norms with a weight that reflects not only how near the point is to the boundary of the domain but also how convex the domain is near the point. We refine and localize the weights that Polking uses in [Po] for the same type of domains because they depend only on the Euclidean distance to the boudary and don't take into account the...

La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici non lineari con l'ambiente. (I) Deduzione di limitazioni a priori sulla temperatura e le sue derivate

Antonio Fasano, Mario Primicerio (1973)

Rendiconti del Seminario Matematico della Università di Padova

Large time regular solutions to the MHD equations in cylindrical domains

Wisam Alame, Wojciech M. Zajączkowski (2011)

Applicationes Mathematicae

We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the L₂-norms of the derivatives of the initial velocity and of the magnetic field with respect to the variable along the axis of the cylinder, we are able to obtain an estimate for the velocity and the magnetic field in $W ₂^{2, 1}$ without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.

Lateral estimates for iterated elliptic operators and analyticity.

Tarama, Shigeo (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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