Abstract
Let be a bounded domain with sufficiently smooth boundary and be a symmetric space defined on the measure space . We consider a Dirichlet problem for ‐th order polyharmonic equation, and we establish its solvability (in strong sense) in Sobolev space generated by the norm of . Such spaces include classical Sobolev spaces, Orlicz–Sobolev spaces, grand Sobolev spaces, and Marcinkiewicz–Sobolev spaces. The obtained results are new for these special cases, too.
Keywords
Mathematics
Sobolev space
Sobolev spaces for planar domains
Dirichlet problem
Sobolev inequality
Polyharmonic spline
Pure mathematics
Mathematical analysis
Dirichlet distribution
Dirichlet's energy
Dirichlet's principle
Interpolation space
Functional analysis
Boundary value problem
Polynomial
Subject Areas
Differential Equations and Boundary Problems
·Applied Mathematics ·Physical Sciences
Spectral Theory in Mathematical Physics
·Mathematical Physics ·Physical Sciences
Advanced Mathematical Modeling in Engineering
·Computational Theory and Mathematics ·Physical Sciences
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