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Michael Hardy
Michael Hardy
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I am interested in determining whether the function $F:L^{\infty}(0,\infty;L^{\infty}(0,1)) \to \mathbb R$ defined by $$u \mapsto F(u)=\int_0^{\infty} \int_0^1 u(x,t)^2 \ \mathrm dx \mathrm dt $$$$u \mapsto F(u)=\int_0^\infty \int_0^1 u(x,t)^2 \ \mathrm dx \, \mathrm dt $$ is differentiable/Frechét differentiable at an element $u \in L^2(0,\infty;L^2(0,1))$.

Any suggestions or assistance would be greatly appreciated.

I am interested in determining whether the function $F:L^{\infty}(0,\infty;L^{\infty}(0,1)) \to \mathbb R$ defined by $$u \mapsto F(u)=\int_0^{\infty} \int_0^1 u(x,t)^2 \ \mathrm dx \mathrm dt $$ is differentiable/Frechét differentiable at an element $u \in L^2(0,\infty;L^2(0,1))$.

Any suggestions or assistance would be greatly appreciated.

I am interested in determining whether the function $F:L^{\infty}(0,\infty;L^{\infty}(0,1)) \to \mathbb R$ defined by $$u \mapsto F(u)=\int_0^\infty \int_0^1 u(x,t)^2 \ \mathrm dx \, \mathrm dt $$ is differentiable/Frechét differentiable at an element $u \in L^2(0,\infty;L^2(0,1))$.

Any suggestions or assistance would be greatly appreciated.

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elmas
elmas
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Differentiation of a norm

I am interested in determining whether the function $F:L^{\infty}(0,\infty;L^{\infty}(0,1)) \to \mathbb R$ defined by $$u \mapsto F(u)=\int_0^{\infty} \int_0^1 u(x,t)^2 \ \mathrm dx \mathrm dt $$ is differentiable/Frechét differentiable at an element $u \in L^2(0,\infty;L^2(0,1))$.

Any suggestions or assistance would be greatly appreciated.