Elliptic Regularity on Convex Domain
$begingroup$
In many literature about elliptic regularity on convex domains, they impose that the domain should be polygonal. (In such cases, the inequality below holds)
However, it seems to me that the polygonal assumption is given to certify regularity of variational(weak) solution rather than inequality.
Question) For convex domain $Omega$ with piecewise smooth boundary, let $u$ be an $H^2$ solution of $Delta u=f$ with $u|_{partialOmega}=0$, does the following 'classical' inequality hold?
$$exists C,s.t.,|u|_{H^2}le C|f|_{H^0}$$
pde elliptic-equations elliptic-operators
asked Jan 5 at 7:30
C.ParkC.Park
1588
$endgroup$
add a comment |
$begingroup$
In many literature about elliptic regularity on convex domains, they impose that the domain should be polygonal. (In such cases, the inequality below holds)
However, it seems to me that the polygonal assumption is given to certify regularity of variational(weak) solution rather than inequality.
Question) For convex domain $Omega$ with piecewise smooth boundary, let $u$ be an $H^2$ solution of $Delta u=f$ with $u|_{partialOmega}=0$, does the following 'classical' inequality hold?
$$exists C,s.t.,|u|_{H^2}le C|f|_{H^0}$$
pde elliptic-equations elliptic-operators
asked Jan 5 at 7:30
C.ParkC.Park
1588
$endgroup$
add a comment |
$begingroup$
In many literature about elliptic regularity on convex domains, they impose that the domain should be polygonal. (In such cases, the inequality below holds)
However, it seems to me that the polygonal assumption is given to certify regularity of variational(weak) solution rather than inequality.
Question) For convex domain $Omega$ with piecewise smooth boundary, let $u$ be an $H^2$ solution of $Delta u=f$ with $u|_{partialOmega}=0$, does the following 'classical' inequality hold?
$$exists C,s.t.,|u|_{H^2}le C|f|_{H^0}$$
pde elliptic-equations elliptic-operators
asked Jan 5 at 7:30
C.ParkC.Park
1588
$endgroup$
In many literature about elliptic regularity on convex domains, they impose that the domain should be polygonal. (In such cases, the inequality below holds)
However, it seems to me that the polygonal assumption is given to certify regularity of variational(weak) solution rather than inequality.
Question) For convex domain $Omega$ with piecewise smooth boundary, let $u$ be an $H^2$ solution of $Delta u=f$ with $u|_{partialOmega}=0$, does the following 'classical' inequality hold?
$$exists C,s.t.,|u|_{H^2}le C|f|_{H^0}$$
pde elliptic-equations elliptic-operators
pde elliptic-equations elliptic-operators
asked Jan 5 at 7:30
C.ParkC.Park
1588
asked Jan 5 at 7:30
C.ParkC.Park
1588
asked Jan 5 at 7:30
C.ParkC.Park
1588
asked Jan 5 at 7:30
C.ParkC.Park
1588
asked Jan 5 at 7:30
C.ParkC.Park
1588
1588
add a comment |
add a comment |
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