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Green's function of Dirichlet problem for biharmonic equation in the ball
Complex Variables and Elliptic Equations, 2018An explicit representation of the Green's function of the Dirichlet problem for the biharmonic equation in the unit ball is given. Expansion of the constructed Green's function in the complete system of homogeneous harmonic polynomials that are ...
V. Karachik
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The Dirichlet problem for thep-fractional Laplace equation
Nonlinear Analysis, 2018We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order s ∈ ( 0 , 1 ) and summability growth p ∈ ( 1 , ∞ ) , whose model is the fractional p -Laplacian operator with measurable ...
Giampiero Palatucci
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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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Dirichlet problem for demi-coercive functionals
Nonlinear Analysis: Theory, Methods & Applications, 1986A class of variational integrals with integrands satisfying a linear growth condition is called by the authors demi-coercive. Example of demi- coercive functionals arise naturally for instance in studying the equilibrium of elastic structures with unilateral constraints on the stress, and in studying the nonparametric Plateau problem.
ANZELLOTTI G +2 more
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An area‐Dirichlet integral minimization problem
Communications on Pure and Applied Mathematics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
I. Athanasopoulos +3 more
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