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Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$

100%

Fiorenza A., Sbordone C.

Studia Mathematica

1998

tom 127

nr 3

223-231

We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here $f ∈ L^1(Ω)$ and the solution belongs to the so-called grand Sobolev space $W_0^{1,2)}(Ω)$. This is the proper space when the right hand side is assumed to be only $L^1$-integrable. In particular, we obtain the exponential integrability of the solution, which in the linear case was previously proved by Brezis-Merle and Chanillo-Li.

The Muckenhoupt class A₁(R)

81%

Bojarski B., Sbordone C., Wik I.

Studia Mathematica

1991-1992

tom 101

nr 2

155-163

It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.

Ograniczanie wyników

2 Studia Mathematica

2 Sbordone C.

1 Bojarski B.

1 Fiorenza A.

1 Wik I.

1 1998

1 1992

Wyniki wyszukiwania

Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$

The Muckenhoupt class A₁(R)