Layering methods for nonlinear partial differential equations of first order

Avron Douglis

Displaying similar documents to “Layering methods for nonlinear partial differential equations of first order”

An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type

Avron Douglis (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Integrability theorems for trigonometric series

Bruce Aubertin, John Fournier (1993)

Studia Mathematica

Similarity:

We show that, if the coefficients (an) in a series $a_{0} / 2 + \sum_{n = 1}^{\infty} a_{n} c o s (n t)$ tend to 0 as n → ∞ and satisfy the regularity condition that $\sum_{m = 0}^{\infty} {\sum_{j = 1}^{\infty} [\sum_{n = j 2^{m}}^{(j + 1) 2^{m} - 1} | a_{n} - a_{n + 1} |] ²}^{1 / 2} < \infty$ , then the cosine series represents an integrable function on the interval [-π,π]. We also show that, if the coefficients (bn) in a series $\sum_{n = 1}^{\infty} b_{n} s i n (n t)$ tend to 0 and satisfy the corresponding regularity condition, then the sine series represents an integrable function on [-π,π] if and only if $\sum_{n = 1}^{\infty} | b_{n} | / n < \infty$ . These conclusions were previously known to hold under stronger restrictions on the sizes...

$L^{p}$ -estimates near the boundary for solutions of the Dirichlet problem

E. B. Fabes, N. M. Riviere (1970)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

$L^{P}$ -uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients

Vitali Liskevich, Michael Röckner, Zeev Sobol, Oleksiy Us (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains

Anna Canale, Patrizia Di Gironimo, Antonio Vitolo (1998)

Studia Mathematica

Similarity:

We introduce a sort of "local" Morrey spaces and show an existence and uniqueness theorem for the Dirichlet problem in unbounded domains for linear second order elliptic partial differential equations with principal coefficients "close" to functions having derivatives in such spaces.

On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

Similarity:

Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^{p} (ℝ)$ -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by $T_{m} f (x) = p . v . \int k (x - y) m (x + y) f (y) d y$ where $k (x) = \sum_{j \in ℤ} 2^{j} φ_{j} (2^{j} x)$ for a family of functions ${φ_{j}}_{j \in ℤ}$ satisfying conditions (1.1)-(1.3) given below.

On functions of finite variation, depending on a parameter

W. Orlicz (1953)

Studia Mathematica

Similarity:

Two-sided estimates of the approximation numbers of certain Volterra integral operators

D. Edmunds, W. Evans, D. Harris (1997)

Studia Mathematica

Similarity:

We consider the Volterra integral operator $T : L^{p} (ℝ^{+}) \to L^{p} (ℝ^{+})$ defined by $(T f) (x) = v (x) ʃ_{0}^{x} u (t) f (t) d t$ . Under suitable conditions on u and v, upper and lower estimates for the approximation numbers $a_{n} (T)$ of T are established when 1 < p < ∞. When p = 2 these yield $l i m_{n \to \infty} n a_{n} (T) = π^{- 1} ʃ_{0}^{\infty} | u (t) v (t) | d t$ . We also provide upper and lower estimates for the $ℓ^{α}$ and weak $ℓ^{α}$ norms of (an(T)) when 1 < α < ∞.