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Showing 1 to 5 of 5 for “"Sobolev embedding"”.
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Supercritical Semi-Linear Elliptic Problems Using Variational Principles
… encountered with nonlinearities that exceed the Sobolev embedding exponent. This enables the effective use of standard variational techniques, leading to existence results for solutions. The work covers two supercritical elliptic problems with different boundary conditions. First, it establishes …
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Smoothing estimates for non commutative spaces
… perspective to establish the noncommutaive Sobolev inequaties (namely, Hardy-Littlewood-Sobolev inequalites), and extend the Sobolev embedding from noncommutative $L_p$ spaces to general Orlicz function spaces related with Cowling and Meda's work. Also we will show some examples to …
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Existence and Stability of Solitary Waves for NLS with Defects
… NLS are in fact exact minimizers of the Sobolev embedding $H^s(\rn)\hookrightarrow L^\infty(\rn)$, which provides an alternative calculation and justification of the sharp constants in these inequalities. Lastly, we consider the degenerate semi-linear Schr\"odinger and Korteweg-de Vries …
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Spatial Decay of Rotating Waves and Restrictions on Finite Disks.
In this thesis, we consider the system of reaction-diffusion equations and the behavior of the solution of such a system. The focus is to concentrate on solutions which decay at infinity. Under suitable assumptions, we prove the solution and its derivatives decay exponentially in all space. We also …