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
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