Index

1-Laplacian, 163

T -accretive operator, 246

T -contraction, 246

ω-limit set, 34

ε-discretization, 227

m-accretive operator, 234

m-completely accretive operator, 244

abstract Cauchy problem, 225

accretive operator, 230

Aronsson-Evans-Wu model for sandpiles,

191

Carlson type inequality, 12

closure of an operator, 224

collapse of the initial condition, 197

completely accretive operator, 243

Crandall-Liggett Theorem, 237

duality map, 231

effective domain, 224

entropy solution of the local p-Laplacian

Neumann problem, 132

explicit solutions for sandpiles models, 200,

219

exponential formula, 237

fast diffusion equation, 238

filtration equation, 238

Fourier splitting method, 90

Fourier transform, 2

fractional Laplacian, 3

fundamental solution, 5

Gaussian, 4

generalized Poincar´ e inequality, 102

Green’s formula, 165

Hausdorff-Young inequality, 3

Hele-Shaw problem, 99

indicator function, 235

infinitesimal generator, 229

Komura Theorem, 235

Lebesgue point, 225

Lumer-Phillips Theorem, 235

main section, 100

mass transport, 210

maximum principle, 104

mild solution, 227

Minty Theorem, 234

monotone operator, 231

Mosco convergence, 241

multivalued operator, 224

nonlocal p-Laplacian problem, 123

with homogeneous Neumann boundary

conditions, 124

nonlocal convection-diffusion equation, 66

Plancherel identity, 3

Poincar´ e type inequality, 100, 137, 144

porous medium equation, 238

Prigozhin model for sandpiles, 214

Radon-Nikodym property, 225

range condition, 237

solution of the nonlocal

p-Laplacian Dirichlet problem, 143

p-Laplacian Neumann problem, 124

Cauchy problem for the p-Laplacian, 154

convection-diffusion problem, 76

Dirichlet total variational flow, 175

linear Cauchy problem, 2

linear homogeneous Dirichlet problem, 31

linear homogeneous Neumann problem,

41

linear nonhomogeneous Dirichlet

problem, 36

linear nonhomogeneous Neumann

problem, 46

Neumann total variational flow, 166

nonlinear Neumann problem, 100

255