• 検索結果がありません。

Menita Carozza, Antonia Passarelli di Napoli  LAHO MA= IKJEI B = ?=II B EA=H AEFJE? IOIJAI

N/A
N/A
Info
ダウンロード
Protected

Academic year: 2022

シェア "Menita Carozza, Antonia Passarelli di Napoli  LAHO MA= IKJEI B = ?=II B EA=H AEFJE? IOIJAI"

Copied!
1
0
0

読み込み中.... (全文を見る)

今ダウンロードする ( 1 ページ )

全文

(1)

Menita Carozza, Antonia Passarelli di Napoli

On very weak solutions of a class of nonlinear elliptic systems

Comment.Math.Univ.Carolinae 41,3 (2000) 493-508.

Abstract: In this paper we prove a regularity result for very weak solutions of equations of the type −divA(x, u, Du) = B(x, u, Du), where A, B grow in the gradient liketp−1andB(x, u, Du) is not in divergence form. Namely we prove that a very weak solution u ∈ W1,r of our equation belongs to W1,p. We also prove global higher integrability for a very weak solution for the Dirichlet problem

{ −divA(x, u, Du) =B(x, u, Du) in Ω, u−uo∈W1,r(Ω,Rm).

Keywords: nonlinear elliptic systems, maximal operator theory

AMS Subject Classification: Primary 35J50, 35J55, 35J99; Secondary 46E30

1

参照

今ダウンロードする ( PDF - 1 ページ - 61.19 KB )

関連したドキュメント

Received02March,2006;accepted08February,2007CommunicatedbyS.S.Dragomir H ( X ) ≡ ( p ( x ) − p ( x ))1 P Threeorfourdecadesago,anumberofresearchersinvestigatedsomeextensionsoftheShan-nonentropy[1].Instatisticalphysics,theTsallisentropy,definedin[10]by 1. I

In the previous paper [6], we gave the uniqueness theorem for the Tsallis entropy for a classical sys- tem, introducing the generalized Faddeev’s axiom.. Then we adopted the

V A N I S H I N G C Y C L E S H E A V E S A N D H O L O N O M I C S Y S T E M S O F D I F F E R E N T I A L E Q U A T I O N S B y M . K a s h i w a r a R e s e a r c h I n s t i t u t e f o r M a t h e m a t i c a l S c i e n c e s K y o t o U n i v e r s

Let R be the abelian category of coherent Dx-MOdules satisfying the conclusion in Proposition 2.. Then we have the

Introduction In this paper we consider the Schr¨odinger equation, with a quadratic derivative term, Lu=t−α|ux|2, t, x∈R u(0, x) =u0(x), x∈R, (1.1) whereL=i∂t+12∂x2, andα∈(0,1)

The methods developed for the nonlinear Schr¨ odinger equations with quadratic nonlinearities u 2 x , | u x | 2 and u 2 x can be applied also to the study of the large time

Introduction and Main Results In this paper, we investigate the dispersive properties of the linear wave equation with an electromagnetic potential (A−B)u=F (t, x)∈[0,∞[×R3, (1.1) wherex= (x1, x2, x3) and A=∂µ∂µ,A

We consider radial solutions to the Cauchy problem for a linear wave equation with a small short-range electromagnetic potential (depending on space and time) and zero initial data1.

In this paper, we consider the existence of periodic solutions of one such system (2) x′(t) +cx′(t−τ) =A(t, x(t))x(t) +f(t, x(t−r1(t

R., Existence theorem of periodic positive solutions for the Rayleigh equation of retarded type, Portugaliae Math.. R., Existence of periodic solutions for second order

(H2)and(H3) h A ( x,u,z ) ,z i≥| z | − c | u | − c (H1) | A ( x,u,z ) |≤ c + c | u | + c | z | , where c , i =1 ,..., 8,and c arepositiveconstants.Thepreviousassumptionsallowustogivethefollowing | B ( x,u,z ) |≤ c + c | u | + c | z | , A :Ω × R × R −→ R a

A fundamental tool in our proof is the choice of a suitable test function, involving level sets of maximal function defined by using a Lemma due to Acerbi and Fusco (see [AF] and

u = − a u + a u +( au ) + f ( u ) , R .Partialdifferentialequationsofthiskindareoftenfoundinthestudyofbiology,chemistry,physicsandengineeringtechnology.Forexample,inthestudyofgrowthanddispersalinpopulations,therearisesthemodelequation[1](2) ,T ]( T> 0), g

Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations..

In this case, x represents the gene type and y(t, a, x) is the distribution of individuals of age a at time t and of gene type x of the population

In [1, 2, 17], following the same strategy of [12], the authors showed a direct Carleman estimate for the backward adjoint system of the population model (1.1) and deduced its