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Entropy methods for reactiondiffusion equations: slowly growing apriori bounds
 Revista Matemática Iberoamericana
"... In the continuation of [DF], we study reversible reactiondiffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropyentropy ..."
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Cited by 29 (21 self)
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entropy dissipation estimate, 2) an explicit global L ∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
A PRIORI BOUNDS FOR SEMILINEAR EQUATIONS AND A NEW CLASS OF CRITICAL EXPONENTS FOR LIPSCHITZ DOMAINS
"... A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains by ..."
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A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains by
A priori bounds via the relative Morse index of solutions of an elliptic system
"... Abstract. We prove a Liouvilletype theorem for entire solutions of the elliptic system −∆u = vq−2v, −∆v = up−2u having finite relative Morse index in the sense of Abbondandolo. Here, p, q> 2 and 1/p + 1/q> (N − 2)/N. In particular, this yields a result on a priori bounds in L ∞ × L ∞ fo ..."
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Cited by 1 (0 self)
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Abstract. We prove a Liouvilletype theorem for entire solutions of the elliptic system −∆u = vq−2v, −∆v = up−2u having finite relative Morse index in the sense of Abbondandolo. Here, p, q> 2 and 1/p + 1/q> (N − 2)/N. In particular, this yields a result on a priori bounds in L ∞ × L
A PRIORI BOUNDS FOR CODIMENSION ONE ISOMETRIC EMBEDDINGS
, 1998
"... Abstract. Let X: (S n, g)→R n+1 be a C 4 isometric embedding of a C 4 metric g of nonnegative sectional curvature on S n into the Euclidean space R n+1. We prove a priori bounds for the trace of the second fundamental form H, in terms of the scalar curvature R of g, and the diameter d of the space ..."
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Cited by 2 (0 self)
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Abstract. Let X: (S n, g)→R n+1 be a C 4 isometric embedding of a C 4 metric g of nonnegative sectional curvature on S n into the Euclidean space R n+1. We prove a priori bounds for the trace of the second fundamental form H, in terms of the scalar curvature R of g, and the diameter d of the space
A Priori Bounds And Renormalized Morse Indices Of Solutions Of An Elliptic System.
"... : We define a "renormalized" Morse index, and prove a BahriLions type result for critical points of E(u;v)= R\Omega fru\Deltarv\GammaH(x;u;v)gdx; i.e. we establish an a priori bound for critical points with bounded Morse index. x1 Introduction and main theorem. In [AV] we obtained exis ..."
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: We define a "renormalized" Morse index, and prove a BahriLions type result for critical points of E(u;v)= R\Omega fru\Deltarv\GammaH(x;u;v)gdx; i.e. we establish an a priori bound for critical points with bounded Morse index. x1 Introduction and main theorem. In [AV] we obtained
On The Trend To Equilibrium For Some Dissipative Systems With Slowly Increasing A Priori Bounds
 J. Statist. Phys
"... . We prove convergence to equilibrium with explicit rates for various kinetic equations with relatively bad control of the distribution tails : in particular, Boltzmanntype equations with (smoothed) soft potentials. We compensate the lack of uniform in time estimates by the use of precise logarithm ..."
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Cited by 33 (9 self)
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. We prove convergence to equilibrium with explicit rates for various kinetic equations with relatively bad control of the distribution tails : in particular, Boltzmanntype equations with (smoothed) soft potentials. We compensate the lack of uniform in time estimates by the use of precise logarithmic Sobolevtype inequalities, and the assumption that the initial datum decays rapidly at large velocities. Our method not only gives explicit results on the times of convergence, but is also able to cover situations in which compactness arguments apparently do not apply (even mere convergence to equilibrium was an open problem for soft potentials). Contents 1. Introduction 1 2. The FokkerPlanck equation with weak drift 7 3. The Landau equation for mollified soft potentials 11 4. The Boltzmann equation for mollified soft potentials 21 References 26 1. Introduction We consider in this work the problem of trend to equilibrium for collisional kinetic equations of the form #f #t = Q(f) (1) w...
A priori bounds for global solutions of a semilinear parabolic problem
 Acta Math. Univ. Comenian
, 1999
"... Consider the problem (P) ut = ∆u+ up−1u, x ∈ Ω, t ∈ (0,∞), ..."
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Cited by 13 (4 self)
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Consider the problem (P) ut = ∆u+ up−1u, x ∈ Ω, t ∈ (0,∞),
Existence results and a priori bounds for higher order elliptic equations and systems
 J. Math. Pures Appl
"... and systems ..."
A PRIORI BOUNDS FOR SOME INFINITELY RENORMALIZABLE QUADRATICS: II. DECORATIONS.
, 2006
"... 2. Yoccoz puzzle, decorations, and the Modified Principal Nest 4 3. Pseudoquadraticlike maps and pseudopuzzle 10 ..."
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Cited by 12 (1 self)
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2. Yoccoz puzzle, decorations, and the Modified Principal Nest 4 3. Pseudoquadraticlike maps and pseudopuzzle 10
LeraySchauder continuation theorems in the absence of a priori bounds
 Topol. Methods Nonlinear Anal
, 1997
"... In 1934, Leray and Schauder have published their fundamental paper Topologie et équations fonctionnelles [37], which is the founding father of algebraic topology in infinitedimensional spaces and a milestone in nonlinear functional analysis and nonlinear differential equations. The style of this ..."
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Cited by 10 (1 self)
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In 1934, Leray and Schauder have published their fundamental paper Topologie et équations fonctionnelles [37], which is the founding father of algebraic topology in infinitedimensional spaces and a milestone in nonlinear functional analysis and nonlinear differential equations. The style
Results 11  20
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286,229