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Results tagged with ap.analysis-of-pdes
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user 10583
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
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1
answer
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Double series solution of wave equation
Let $u(x,y,t)$ be the solution of wave equation $u_{tt}=u_{xx}+u_{yy}, 0\lt x\lt 1, 0\lt y\lt 1, t\ge 0,$ $u(x,y,0)=(x-x^2)(y-y^2), u_t(x,y,0)=0$ and $ u(x,y,t)=0$ on the boundary of the square. Then …
- 744
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analysis question related to $L^p$ type inequalities
If $p=2n$, a positive even integer, then your inequality is true -- use polar coordinates.
In view of this fact, I think your inequality should be true for all $p>1$.
- 744