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We consider a function $u : Ω \to ℝ^{N}$ , $Ω \subset ℝ^{n}$ , minimizing the integral $\int_{Ω} (| D_{1} {u |}^{2} + \dots + | D_{n - 1} {u |}^{2} + | D_{n} u |^{p}) d x$ , $2 (n + 1) / (n + 3) \leq p < 2$ , where $D_{i} u = \partial u / \partial x_{i}$ , or some more general functional with the same behaviour; we prove the existence of second weak derivatives $D (D_{1} u), \dots, D (D_{n - 1} u) \in L^{2}$ and $D (D_{n} u) \in L^{p}$ .

Diffusion and cross-diffusion in pattern formation

Wei-Ming Ni (2004)

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

We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as $2 \times 2$ systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.

Dini-Campanato spaces and applications to nonlinear elliptic equations.

Kovats, Jay (1999)

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

Dirichlet problem for quasi-linear elliptic equations.

Baalal, Azeddine, Rhouma, Nedra BelHaj (2002)

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

Discontinuous elliptic problems in $ℝ^{N}$ without monotonicity assumptions

Silvia Cingolani, Monica Lazzo (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove existence of a positive, radial solution for a semilinear elliptic problem with a discontinuous nonlinearity. We use an approximating argument which requires no monotonicity assumptions on the nonlinearity.

Displaying 1 – 13 of 13

Das Verhalten von Lösungen semilinearer elliptischer Systeme an Ecken eines Gebietes.

Decaying Entire Positive Solutions of Quasilinear Elliptic Equations.

Decaying positive entire solutions of the $p$ -Laplacian

Differentiability and partial Hölder continuity of the solutions of non-linear elliptic systems of order $2 m$ with quadratic growth

Differentiability for minimizers of anisotropic integrals

Diffusion and cross-diffusion in pattern formation

Dini-Campanato spaces and applications to nonlinear elliptic equations.

Dirichlet problem for quasi-linear elliptic equations.

Discontinuous elliptic problems in $ℝ^{N}$ without monotonicity assumptions

Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation.

Domain identification for semilinear elliptic equations in the plane: The zero flux case.

Doubly nonlinear parabolic equations related to the $p$ -Laplacian operator.

Duality and best constant for a Trudinger–Moser inequality involving probability measures

Currently displaying 1 – 13 of 13