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"We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form inhomogeneous equations, and also continuity of weak solutions to homogeneous equations. For example, we consider the family {f[sigma]}[sigma]>0 with f[sigma] (x) = e -( 1 [pipe]x[pipe] ) [sigma] , -[infinity]
Differential equations, Elliptic
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Function spaces.
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Partial differential equations -- Qualitative properties of solutions -- Smoothness and regularity of solutions to PDEs.
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Partial differential equations -- Generalized solutions -- Weak solutions to PDEs.
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Partial differential equations -- Close-to-elliptic equations -- None of the above, but in this section.
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Geometry -- Metric geometry -- None of the above, but in this section.
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Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems.
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Numerical solutions.
Choose an application
"We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form inhomogeneous equations, and also continuity of weak solutions to homogeneous equations. For example, we consider the family {f[sigma]}[sigma]>0 with f[sigma] (x) = e -( 1 [pipe]x[pipe] ) [sigma] , -[infinity]
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