Bounded domain Mathematical operators 4 1-Laplacian 2 Antimaximum principle 2 Basic results 2 CHEEGER constant 2 Cheeger 2 Cheeger constant 2 Compactly supported 2 Counter examples 2 Critical Sobolev exponent 2 Critical growth 2 Diffusion 2 Dirichlet boundary condition 2 Dirichlet problem 2 Divergence operator 2 Divergence operators 2 Eigenvalues and eigenfunctions 2 Existence of Solutions 2 Explicit formula 2 Holmium 2 Hölder-α domains 2 Laplace equation 2 Laplace transforms 2 Lipschitz domain 2 Maximum principle 2 Mean values 2 Multiple solutions 2 Nonlinear equations 2 Nonlocal 2