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| REGULARITY ESTIMATES FOR THE OBLIQUE DERIVATIVE PROBLEM ON NON-SMOOTH DOMAINS (I) |
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Citation： |
Guan Pengfei,E. Sawyer.REGULARITY ESTIMATES FOR THE OBLIQUE DERIVATIVE PROBLEM ON NON-SMOOTH DOMAINS (I)[J].Chinese Annals of Mathematics B,1995,16(3):299~324 |
| Page view： 1350
Net amount： 789 |
Authors： |
Guan Pengfei; E. Sawyer |
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| Abstract： |
The authors consider the existence and regularity of the oblique
derivative problem:
$$
\left\{
\aligned
Pu & = f \quad \roman{in}\ \Omega, \ \overset{\rightarrow }\to{\ell }u & = g \quad
\ \roman{on}\ \partial\Omega,
\endaligned
\right.
$$
where $P$ is a second order elliptic differential operator
on $R^n$, $\Omega $ is a bounded domain in $R^n$ and
$\overset{\rightarrow }\to{\ell }$ is a unit vector field
on the boundary of $\Omega $ (which may be tangential to
the boundary). All above are assumed with
limited smoothness.
The authors show that solution $u$ has an
elliptic gain from $f$ in
Holder spaces ( Theorem 1.1). The authors obtain $L^p$
regualrity of
solution in Theorem 1.3, which generalizes the results in
[7] to the limited smooth case. Some of the application
nonlinear problems are also discussed. |
Keywords： |
Oblique derivative, Degenerate boundary value problem,Existence,Regularity. |
Classification： |
35J25, 35B65, 35J65 |
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