Extremals in nonlinear potential theory

Abstract We consider the PDE - Δ p ⁢ u = ρ -\Delta_{p}u=\rho , where 𝜌 is a signed Borel measure on R n \mathbb{R}^{n} . For each p > n p>n , we characterize solutions as extremals of a generalized Morrey inequality determined by 𝜌.

Weak Barriers in Nonlinear Potential Theory

Potential Analysis ◽

10.1007/s11118-007-9064-2 ◽

2007 ◽

Vol 27 (4) ◽

pp. 381-387 ◽

Cited By ~ 4

Author(s):

Anders Björn

Keyword(s):

Potential Theory ◽

Nonlinear potentials in function spaces

Nagoya Mathematical Journal ◽

10.1017/s0027763000008163 ◽

2002 ◽

Vol 165 ◽

pp. 91-116 ◽

Cited By ~ 1

Author(s):

Murali Rao ◽

Zoran Vondraćek

Keyword(s):

Banach Space ◽

Potential Theory ◽

Finite Energy ◽

Duality Mapping ◽

Quadratic Functional ◽

Continuous Linear ◽

Linear Functionals ◽

Nonlinear Potential ◽

Nonlinear Potentials

We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capacities, equilibrium potentials and measures of finite energy.

Nonlinear potential theory on the ball, with applications to exceptional and boundary interpolation sets.

10.1307/mmj/1029005154 ◽

1995 ◽

Vol 42 (1) ◽

pp. 79-97 ◽

Cited By ~ 7

Author(s):

W. S. Cohn ◽

I. E. Verbitsky

Keyword(s):

Potential Theory ◽

Boundary Interpolation ◽

Weighted nonlinear potential theory

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1986-0849468-4 ◽

1986 ◽

Vol 297 (1) ◽

pp. 73-73 ◽

Cited By ~ 24

Author(s):

David R. Adams

Keyword(s):

Potential Theory ◽

On the Edge Singularity of an Actuator Disk with Large Constant Normal Load

Journal of Ship Research ◽

10.5957/jsr.1977.21.2.125 ◽

1977 ◽

Vol 21 (02) ◽

pp. 125-131

Author(s):

G. H. Schmidt ◽

J. A. Sparenberg

Keyword(s):

Potential Theory ◽

Normal Load ◽

Curved Surface ◽

Singular Behavior ◽

Edge Singularity ◽

Actuator Disk ◽

Nonlinear Potential ◽

Constant Normal Load ◽

Special Case

In this paper some aspects of the nonlinear potential theory of actuator disks are considered. A rather general formulation of the problem for a prescribed load on a curved surface is given. For the special case of constant normal load and no incoming velocity the singular behavior of the flow at the edge of the disk is discussed.