Displaying similar documents to “ L ∞ -estimates for solutions of nonlinear parabolic systems with gradient linear growth”

L ∞ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

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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 ∞ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, L ∞ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The L ∞ -estimates are obtained by the Di Benedetto methods.

Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities II. Local and global solvability results

Arina A. Arkhipova (2001)

Commentationes Mathematicae Universitatis Carolinae

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We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution is smooth almost everywhere and has an at most finite number of singular points.

On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions

Joachim Naumann, Jörg Wolf, Michael Wolff (1998)

Commentationes Mathematicae Universitatis Carolinae

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We prove the interior Hölder continuity of weak solutions to parabolic systems ∂ u j ∂ t - D α a j α ( x , t , u , ∇ u ) = 0 in Q ( j = 1 , ... , N ) ( Q = Ω × ( 0 , T ) , Ω ⊂ ℝ 2 ), where the coefficients a j α ( x , t , u , ξ ) are measurable in x , Hölder continuous in t and Lipschitz continuous in u and ξ .

Growth of the product ∏ j = 1 n ( 1 - x a j )

J. P. Bell, P. B. Borwein, L. B. Richmond (1998)

Acta Arithmetica

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We estimate the maximum of ∏ j = 1 n | 1 - x a j | on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when a j is j k or when a j is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when a j is j.    In contrast we show, under fairly general conditions, that the maximum is less than 2 n / n r , where r is an arbitrary positive number. One consequence...

On a discrete version of the antipodal theorem

Krzysztof Oleszkiewicz (1996)

Fundamenta Mathematicae

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The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping f : S k → ℝ k there exists a point x ∈ S k such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which S k is replaced by the set of vertices of a high-dimensional cube equipped with Hamming’s metric. In place of equality we obtain some optimal estimates of i n f x | | f ( x ) - f ( - x ) | | which were previously known (as far as the author knows) only for f linear (cf. [1]).

The Lucas congruence for Stirling numbers of the second kind

Roberto Sánchez-Peregrino (2000)

Acta Arithmetica

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0. Introduction. The numbers introduced by Stirling in 1730 in his Methodus differentialis [11], subsequently called “Stirling numbers” of the first and second kind, are of the greatest utility in the calculus of finite differences, in number theory, in the summation of series, in the theory of algorithms, in the calculation of the Bernstein polynomials [9]. In this study, we demonstrate some properties of Stirling numbers of the second kind similar to those satisfied by binomial coefficients;...