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Results tagged with sobolev-spaces
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user 60869
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
4
votes
1
answer
196
views
Introduction to free boundary problems (that are not Stefan problems)
Could someone recommend some notes/papers that deal with existence/regularity of free boundary problems arising from parabolic equations (excluding Stefan type equations)?
I am thinking of eg. degene …
- 93
3
votes
0
answers
185
views
Existence of solution to weak form of linear equation with boundary integral (parabolic PDE)
Let $W(0,T) := \{ u \in L^2(0,T;H^{\frac 12}(\partial\Omega)) \mid u_t \in L^2(0,T;H^{-\frac{1}{2}}(\partial\Omega))\}$. Let $\gamma$ and $\xi$ denote the trace map and its right inverse.
Does there …
- 93
1
vote
0
answers
88
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Regularity of solutions to $u' + Au = f$ for nonlinear monotone operator $A$
Consider the equation
$$u' + Au = f$$
$$u|_{\partial \Omega} = 0$$
$$u(0) = u_0$$
where $A:L^p(0,T;W^{1,p}_0) \to L^q(0,T;W^{-1,q})$ is some monotone nonlinear operator (with additional assumptions). …
- 93
1
vote
1
answer
259
views
Image of (right) inverse trace map $\xi\colon H^{\frac 12}(\partial\Omega) \to H^1(\Omega)$ ...
Let $\gamma\colon H^1(\Omega) \to H^{\frac 12}(\partial\Omega)$ be the linear trace map which has a right continuous inverse $\xi\colon H^{\frac 12}(\partial\Omega) \to H^1(\Omega)$.
Is the image of …
- 93