Interior Differentiability Results for Nonlinear Variational Parabolic Systems with Nonlinearity q in ]1,2[
Articolo
Data di Pubblicazione:
2011
Abstract:
In this work we prove that the solutions
${\scriptstyle u\in L^{q}(-T,0,H^{1,q}(\Omega,\RR^{N}))\cap
C^{0,\lambda}(\overline{\!Q},\RR^{N})}$
${\scriptstyle (1
system of variational type
$${\scriptstyle -\sum_{j=1}^{n}D_{j}a^{j}(X,u,Du)+{\partial u\over\partial t}=
B^{0}(X,u,Du)\;,\quad X=(x,t)\in Q\,,}$$
belong to the space
${\scriptstyle L^{q}(-a,0,H^{2,q}_{\loc}(\Omega,\RR^{N}))\cap
H^{1,q}(-a,0,L^{q}_{\loc}(\Omega,\RR^{N}))}$,
for all ${\scriptstyle a\in]0,T[}$, provided suitable hypotheses of
${\scriptstyle q}$-nonlinearity
${\scriptstyle (1
${\scriptstyle u\in L^{q}(-T,0,H^{1,q}(\Omega,\RR^{N}))\cap
C^{0,\lambda}(\overline{\!Q},\RR^{N})}$
${\scriptstyle (1
system of variational type
$${\scriptstyle -\sum_{j=1}^{n}D_{j}a^{j}(X,u,Du)+{\partial u\over\partial t}=
B^{0}(X,u,Du)\;,\quad X=(x,t)\in Q\,,}$$
belong to the space
${\scriptstyle L^{q}(-a,0,H^{2,q}_{\loc}(\Omega,\RR^{N}))\cap
H^{1,q}(-a,0,L^{q}_{\loc}(\Omega,\RR^{N}))}$,
for all ${\scriptstyle a\in]0,T[}$, provided suitable hypotheses of
${\scriptstyle q}$-nonlinearity
${\scriptstyle (1
Tipologia CRIS:
1.1 Articolo in rivista
Keywords:
Non linear parabolic systems; interior differentiability; interpolation inequalities
Elenco autori:
Fattorusso, Luisa Angela Maria; M., Marino
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