Parabolic Quasilinear Equations Min-imizing Linear Growth Functionals

By F. Andreu-Vaillo, V. Caselles, José M. Mazón. 2004

431 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/a3622204d5a8ebcfa4c592665f9dd6b231274088

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM (2007, background): “But it turns out that the structure of the elements of ∂E(u) can be derived if BV (Ω) ∩ Lp(Ω) is considered as a subspace of Lp(Ω) and if E is extended on Lp(Ω) in a trivial way, cf. AndreuVaillo, Casseles & Mazón [4] and references therein.”
A nonlocal p-Laplacian evolution equation with Neumann boundary conditions (2008, background): “ProblemN1(u0), that is, the Neumann problem for the total variation flow, was studied in [2] (see also [3]), motivated by problems in image processing.”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “etation in terms of total variation ow for signed data, see [40] in 1D and compare with [209]. Total variation ow is an very important subject in itself, related to the p-Laplacian, cf. the monograph [7]. Super-fast diffusion. Once we cover m= 0 the natural question is, can we cover m<0. Actually”
On the behaviour of the solutions to p-Laplacian equations as p goes to 1 (2008, methodology): “= f in BR, u = 0 on ∂BR, in the sense of the definition given in [4], [6], [5].”
Variable Exponent, Linear Growth Functionals in Image Restoration (2006, background): “More related work on linear-growth functionals and their flows can be found in [2, 3, 4, 5, 6, 7, 12, 14, 33].”
Fractional p-Laplacian evolution equations (2016, background): “Let us now do the proof for the singular case p = 1 which is a little different from the previous case since the boundary values are taken now in a weaker sense, see the expression of Φ above (see [2] for more details on how the Dirichlet boundary conditions must be considered for the Dirichlet prob”
The Cauchy problem for a strongly degenerate quasilinear equation (2005, background): “A generalized Green formula We shall need several results from [8] (see also [3]) in order to give a meaning to integrals of bounded vector fields with divergence in L1 integrated with respect to the gradient of a BV function.”
A Strongly Degenerate Quasilinear Equation: the Parabolic Case (2005, background): “The case of equations of type ∂u ∂t = div a(x,Du) in (0, T )×Ω, (6) where a(x, ξ) = ∇ξf(x, ξ), f(x, ·) being a convex function of ξ with linear growth as ‖ξ‖ → ∞ has been considered in [2], [3] and [4] (see also [6]), where existence and uniqueness results of entropy solutions were proved.”
Radial equivalence for the two basic nonlinear degenerate diffusion equations (2008, background): “Keywords: Porous medium equation; p-Laplacian equation; Radially symmetric solutions; Self-similar solutions; Phase-plane analysis; Anomalous exponents”