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The Dirichlet Eigenvalue Problem for Elliptic Systems on Domains with Thin Tubes
, 2010 Justin L. Taylor
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Polyharmonic dirichlet problems
Proceedings of the Steklov Institute of Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Begehr, H., Vu, T. N. H., Zhang, Z.-X.
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Superlinear Dirichlet problems
Nonlinear Analysis: Theory, Methods & Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Quasi-Linear Relaxed Dirichlet Problems
SIAM Journal on Mathematical Analysis, 1996This work is devoted to the study of quasilinear relaxed Dirichlet problems that can ``formally'' be written as \[ -\Delta u+\lambda_0u+\mu u= f(x,u,Du)\quad\text{in }\Omega,\quad u=0\quad\text{on }\partial\Omega, \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\), \(\lambda_0\geq 0\), \(f\) satisfies a quadratic growth condition with respect ...
Finzi Vita, Stefano +2 more
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Relaxation for Dirichlet Problems Involving a Dirichlet Form
Zeitschrift für Analysis und ihre Anwendungen, 2000For a fixed Dirichlet form, we study the space of positive Borel measures (possibly infinite) which do not charge polar sets. We prove the density in this space of the set of the measures which represent varying, domains. Our method is constructive. For the Laplace operator, the proof was based on a pavage of the space.
BIROLI, MARCO, TCHOU N.
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2020
The exterior Dirichlet problem consists in finding u such that $$\displaystyle \begin {array}{rl} &Au(x)=0,\quad x\in S^-,\\ &u(x)=\mathscr {D}(x),\quad x\in {\partial S},\\ &u\in \mathscr {A}^*, \end {array} $$ where the vector function \(\mathscr {D}\in C^{(1,\alpha )}({\partial S})\), α ∈ (0, 1), is prescribed.
Christian Constanda, Dale Doty
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The exterior Dirichlet problem consists in finding u such that $$\displaystyle \begin {array}{rl} &Au(x)=0,\quad x\in S^-,\\ &u(x)=\mathscr {D}(x),\quad x\in {\partial S},\\ &u\in \mathscr {A}^*, \end {array} $$ where the vector function \(\mathscr {D}\in C^{(1,\alpha )}({\partial S})\), α ∈ (0, 1), is prescribed.
Christian Constanda, Dale Doty
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2020
The interior Dirichlet problem consists of the equation and boundary condition $$\displaystyle \begin {array}{ll} &Au(x)=0,\quad x\in S^+,\\ &u(x)=\mathscr {D}(x),\quad x\in {\partial S}, \end {array} $$ where the vector function \(\mathscr {D}\in C^{1,\alpha }({\partial S})\), α ∈ (0, 1), is prescribed.
Christian Constanda, Dale Doty
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The interior Dirichlet problem consists of the equation and boundary condition $$\displaystyle \begin {array}{ll} &Au(x)=0,\quad x\in S^+,\\ &u(x)=\mathscr {D}(x),\quad x\in {\partial S}, \end {array} $$ where the vector function \(\mathscr {D}\in C^{1,\alpha }({\partial S})\), α ∈ (0, 1), is prescribed.
Christian Constanda, Dale Doty
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2001
In its simplest form the Dirichlet problem may be stated as follows: for a given function \( f \in C\left( {{\partial ^\infty }\Omega } \right)\), determine, if possible, a function h ∈ H(Ω) such that h(x) → f(y) as x → y for each \( y \in {\partial ^\infty }\Omega \).
David H. Armitage, Stephen J. Gardiner
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In its simplest form the Dirichlet problem may be stated as follows: for a given function \( f \in C\left( {{\partial ^\infty }\Omega } \right)\), determine, if possible, a function h ∈ H(Ω) such that h(x) → f(y) as x → y for each \( y \in {\partial ^\infty }\Omega \).
David H. Armitage, Stephen J. Gardiner
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