The existence or nonexistence of solutions for some equations involving weighted critical exponents on the unit ball

<abstract><p>This paper deals with the new Fujita type results for Cauchy problem of a quasilinear parabolic differential inequality with both a source term and a gradient dissipation term. Specially, nonnegative weights may be singular or degenerate. Under the assumption of slow decay on initial data, we prove the existence of second critical exponents $ \mu^{*} $, such that the nonexistence of solutions for the inequality occurs when $ \mu < \mu^{*} $.</p></abstract>

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EXISTENCE AND REGULARITY FOR A QUASILINEAR ELLIPTIC EQUATION INVOLVING CRITICAL EXPONENTS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30341-2 ◽

1989 ◽

Vol 9 (2) ◽

pp. 149-162 ◽

Cited By ~ 1

Author(s):

Jianfu Yang

Keyword(s):

Elliptic Equation ◽

Critical Exponents ◽

Quasilinear Elliptic Equation ◽

Quasilinear Elliptic

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Critical exponents for Ising-like systems on Sierpinski carpets

Journal de Physique ◽

10.1051/jphys:01987004804055300 ◽

1987 ◽

Vol 48 (4) ◽

pp. 553-558 ◽

Cited By ~ 35

Author(s):

B. Bonnier ◽

Y. Leroyer ◽

C. Meyers

Keyword(s):

Critical Exponents ◽

Sierpinski Carpets

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On Dirichlet type spaces on the unit ball of Cn

Annales Universitatis Mariae Curie-Sklodowska sectio A – Mathematica ◽

10.2478/v10062-011-0015-4 ◽

2011 ◽

Vol 65 (2) ◽

Author(s):

Małgorzata Michalska

Keyword(s):

Unit Ball ◽

Dirichlet Type ◽

Type Spaces ◽

Dirichlet Type Spaces

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Holomorphically embedded discs with rapidly growing area

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500021399 ◽

1999 ◽

Vol 129 (2) ◽

pp. 343-349

Author(s):

Josip Globevnik

Keyword(s):

Unit Ball ◽

Open Unit ◽

Open Unit Ball

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.

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