H�lder classes with boundary conditions as interpolation spaces

Three-phase boundary motion by surface diffusion: stability of a mirror symmetric stationary solution

“…, where C τ is a constant depending onξ(τ ), v(τ, ·) C 2+α [0,1] . Then, by means of (A.3) and using this inequality, we get A (2) τ U X α C eq,τ A .…”

“…First, we prove that A τ is a sectorial operator in X . As stated above, it is known that A (1) τ is a sectorial operator in X (see [26] where C is a constant independent of U . In fact, one can prove…”

“…In particular, we can verify that a constant C 0 increases with 1/ξ 0 , v 0 C 2+α [0,1] . Hereafter any constant depending on these quantities will be denoted by C 0 .…”

Nonlinear Stability of Stationary Solutions for Surface Diffusion with Boundary Conditions

“…Using (B.1) with k = 0 and β 1 = β 2 = (2+α)/4 to ρ 1 , and with k = 1, β 1 = (2+α)/4, and β 2 = α/4 to ∂ρ 1 This means that if we obtain the estimates for dz/dt, we have the desired estimates for ρ 3 . In fact, the estimate for ρ 3 Y(Q 0,T ) is given by ) .…”

“…[1,17,18]) and the definition of where C 0 and M 0 depend on ρ 0 C 2+α (I) increasingly, and C 0,K and N 0,K depend on ρ 0 C 2+α (I) and K increasingly. This completes the proof of Lemma A.1(i).…”